This WILL have spoilers, but this show doesn't really have spoilers per se.
Let's start off by describing my experience with Fate and the Extraverse. This is also simple, and is as follows:

• Notes: Masterpiece.
• Fate/stay night VN: Close to a masterpiece. Some writing choices make this at least a 9.5 for me.
• FGO: Don't play it.
• Fate/Extra: Doesn't suck, but isn't good. Its execution is flawed, but the ideas are definitely there. Story average, characters and worldbuilding good. Gameplay horrible.

Make a note here, because unlike every other watcher, I've actually played what's necessary to understand what's going on in this anime from just the first two episodes, if not understand the entire show.

Plot

Simple and effective. The first episode is quite easy to follow. It's meant to throw us off into thinking this is a basic, normal Extra adaptation. There are multiple clues to stop us from thinking such, but for now, we'll ignore those. They aren't really important to understanding the plot but more like foreshadowing. It's a 1:1 mirror to the "tutorial" MC NPC in Fate/Extra that dies when you get rekt by the Automata while trying to leave the preliminary stratum.

The second episode is when the actual plot is shown to us. Straightforward. Hakunon, from the original Fate/Extra canon, failed. She lost to Twice Pieceman after rejecting his offer. Now Saver's Noble Phantasm, the Chakravartin, has killed/brought about the slow and inevitable demise of the Moon Cell, causing each strata to become a floor, and each hold a Floor Master. We now know this takes place at a "bad end" to the original Fate/Extra, so most should have stopped here because they wouldn't understand anything past this point. I honestly have no clue why people kept going, but Fate anime-onlies and seasonal watchers are crazy unpredictable people so its probably that.
This sequence of events, in itself, is enough to clue you in about a couple of things. Using our knowledge of Fate/Extra, you'd realize that in the first place if Hakunon reached Twice Pieceman, then every HGW participant should be dead. Because Twice Pieceman is the final participant/boss of the Extra HGW, so logically every other participant has already been eliminated. And from the first episode its obvious that they aren't. In fact, instead of different participants, these are the exact same people Hakunon should have killed. This is explained later, but you wouldn't even notice this without playing Extra.

That's pretty much the plot. It's not that complicated, though it requires that knowledge from Extra. The main issue I have with this, is that in basically every review of this show, people state that yes, they've played it, but the plot is still a complete mystery to them. They have not played it. These concepts are explained by the game itself, and the fact that you NEED to know what happens in Extra is evident in the first scene of the first episode. IT IMMEDIATELY BEGINS WITH THE END OF EXTRA. Aside from this fact, the title itself is a dead giveaway. Here's the definition of Encore in English:

a repeated or additional performance of an item at the end of a concert, as called for by an audience.

A Last Encore would, evidently, mean that its the last performance. That would mean there was a performance before it. Because this is the last one, of course.
Let's try it with the French usage of the word. I don't really need a definition for this, but its basically just "again," in most circumstances. A Last Encore would then mean trying again for the last time. This would mean there was an initial attempt that failed. In the midst of Isekai sentences that describe the plot entirely, this title is refreshing and actually represents the show.

In relation to criticism and analysis of the plot itself, it serves as a wagon for the characters to move on, and to develop Twice Pieceman as an antagonist because Extra just made him out to be big bad man for the most part. There really isn't much to tackle as the plot is hardly the main focus, as likewise in-game, so nothing outstanding. If I had to score it, it would probably be around a 6.5/10.
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Characters
The shining highlight and Nasu's strength. Let's go back to episode one. Remember Hakunon dying and then Hakuno showing up in the preliminary stratum? Yes, this is a different Hakuno. He isn't what he seems to be, because of the weird events of the first episode.

every HGW participant should be dead

Here we get to see Leo, Rin, and Shinji as returning characters... but as mentioned, they should be dead. Same with Hakuno, because Hakunon is also dead. And the exact same with every single Floor Master. This is very important. I'll be focusing mostly on Hakuno here because he's the MC and gets the most development but each Floor Master should not be shafted (I'm only doing so to attempt at conciseness). Each of them is changed, different, or better than their Extra counterparts. They each have their own unique quirks, their own unique Floor which complements their separate theme amazingly, improved by SHAFT animation, but we'll get to that part later.

HAKUNO Kishinami (Extra art because it's raw)

The themes of the MC are really striking as well-written, and logically follow a sense of development. It goes from "What it means to be alive," to "Why should we keep living if so?" and then lastly "Even if I may not be human myself, are they worth saving?" There is a thematic progression had here, and as he progresses each Floor, smoothly in such a way as not clearly describing it to the audience, but instead through the visual animation and the Floor Master. He's a unique character, and the Dead Face aspect just adds more to each of these themes. Is he really alive if he's just a bunch of hating souls? Why ascend, without a goal? Can he really save humanity if he serves to hate such?

His cleaner, less annoying relationship with Nero also ascends her character and their interactions for me. Nero serves as a sort of "mentor-ish" role to him, providing advice from her life as emperor and her experience in order to fuel his character growth. As this goes on, he starts warming up to her a lot more. He becomes more expressive toward her, instead of his constant deadpan delivery which is seen in the beginning.

Nero (Red Saber)

Is actually bearable. I know, I know. Impossible, right? But yes, they've done it. Unlike Extra, Nero serves a much bigger purpose in the overall narrative, mostly in helping Hakuno through his character struggles. Her dialogue is also much less annoying and preachy, putting the constant UmU aside (no Padoru posters). To the Nero haters, I'm a part of you, but just give her a chance here. Her fan-service is sometimes a bit... obnoxious. I wouldn't expect otherwise from any entry in the Extraverse as sex is a huge part for some reason (thanks CCC), so it just comes hand-in-hand. Oh yea, her backstory was an extremely nice touch. Her motivations became clearer, and it made her not feel like the complete caricature she was in Fate/Extra.

I wish I could spend more lines on each Floor Master, but it would take way too long and it's simply tiring. I would rather someone experience it themselves rather than describing how depressing Alice's Floor was, or just how much Leo had given up on his entire sense of self. For the score, I would give a 10/10 in this section.
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Visuals/Sound Design
It's SHAFT. They have a reputation.
Anyway, they're a vast improvement on whatever the fuck the copy-paste levels were in Extra. Each Floor is finely attuned to each Floor Master, bringing about visuals unlike I've ever seen from anime. They each represent a different part of the Floor Master, being a metaphor to such, unlike the original. Aside from the stunning backgrounds, THERE'S LIKE ZERO CGI. It's probably the happiest I've been watching modern-esque anime. And even more so then that, the amount of frames is fucking stunning. There were zero instances where I questioned the quality, in fact, this anime is basically what Apoc should have been. A consistently well-animated all across the board show, with each fight scene being as stunning as the last, instead of cramming all that effort in the last 5 episodes. It's very overblown, and over the top, just as a Fate anime should be. No ufotable CGI sparks here, or directionless Babylonia animation wank. 9/10.

The sound design is... good for what it is. There are specific tracks that sound more orchestra-based that I enjoy much more and think they are perfect for their use, but a lot of the electronic-sounding ones are extremely bad. The sound mixing is average, there's no wubs or anything of the sort this time around. The music complements what's happening, nothing bad there. Slightly above average, but not enough to blow me away or anything. 6.5/10.
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Direction/Pacing
It's very well-paced, keeping me glued to the screen the entire time I was watching. There are no points with stand-still exposition, it usually has a moving element in typical SHAFT fashion, in order to keep the viewer somewhat entertained visually while they are explaining some concepts/need to know info (for example, in the second episode when Rin explains Wizards). The Floors each take about 2 episodes each. They start off with introductions of the Floor and development of the Floor Master in the first episode, and then in the second, they apply that to Hakuno, the current plot, situation seamlessly. It sounds formulaic on paper, but its execution is fantastic. This is one of my favorites aspects of the show, how you can feel its video-gamey-ness but it constantly reminds you that it's trying to go beyond it and is, in fact, a very well made anime, one attuned to its finest strings. 9/10.
One common criticism I hear is that the Tamano floor was done off-screen, but the thing is, it would have broken the currently existing pacing. It was unnecessary and would have not done anything for Hakuno, which is why it was mentioned in the optional Drama CD.
#The juicy shit
So as you read this review, you may be wondering "How is this only a 6/10 average while this guy seems to be having the time of his life?"
A normal question, and for those who are familiar with the franchise, a predictable answer. Type-Moon has no clue how to market, or what the fuck they are doing.

Marketing

The real bad stuff. The first mistake was implying in any way that this is an adaptation of the PSP game Fate/Extra in its marketing. It's clearly not, because if it was, this would not be so confusing to some. Viewers came into the anime thinking it was because of the marketing, and came out extremely confused. Because its really not an adaptation of Extra, but more of a complementary piece that uses pre-established elements/concepts to create a semi-similar but extremely different narrative. So yes, when watching this seasonally, people weren't happy, dropped it, reviewed it like shit, etc etc. I won't put this as entirely their fault, BUT I will blame them for continuing to watch after lore was thrown around that they didn't understand and was never explained in the show (because it was in the game)

The second mistake was... making an anime for an old PSP game, without giving any access to it currently, aside from the manga adaptation (which is subpar anyways). This way, Last Encore would be the only modern entryway into the Extraverse, as Extella is more of a spin-off that uses a separate timeline and separate lore. So even more people wouldn't be aware of how to properly experience it. Type-Moon is horrible at this, its a trend honestly.

The reviews, ratings, and mass-spread ignorance

In order to put fuel on the dumpster fire that was the marketing, the reviewers did not make it any better. This was indeed badly reviewed, but also in extremely bad faith. Fate haters took the opportunity to do their thing as expected, but that isn't really relevant. What was, were the fake fans, which we will call "fakers." Taken from the top-rated review on MAL:

Oh boy, Fate/Extra: Last Encore. I should say, right off the bat, that while I am a fan of the Fate universe... So I decided to give this a shot anyway. Why not? It has an alluring premise and takes place in an alternate timeline to Fate/stay night. In this timeline, mana have disappeared and Wizards are forced to use virtual space for magic. Similar to some of the other Fate series, a Holy Grail War is set up by a computer that pits 128 Masters in a tournament. The winner will be chosen with a wish to be granted by the Moon Cell Automaton, a mysterious computer of unimaginative powers. Main male protagonist Makuno Kishinami gets caught up into this battle for survival and is clueless on why he is involved. Luckily for him, he gets a servant called Saber. (do note for the sake of avoiding spoilers, I’ll just refer her as “Red Saber” from now on)

Has not played the video game. Gets the basic plot summary wrong...

If you’re hoping some of your favorite Fate character to show up in this series, then prepare for disappointment. Only a small handful of characters like Rin, Sakura, and Shinji appear and most of their roles are downplayed to get over the main cast. Some of the characters from Fate/Grand Order game also shows up although their roles are so small that you’ll likely forget them incredibly easily. Most of the minor characters have their roles minimized and episodes’ resolutions feel rushed.

Proceeds to think Fate/Extra is connected to Fate/stay night...

What bugs me though is how the main plot is executed with Hakuno and Red Saber as the main characters. Don’t me wrong. They are highly entertaining to watch at first but after a while, you may wonder if it’s worth investing time into them at all... But the series’ main story is not abominable. It’s actually much worse. For the majority of viewers, you’ll probably scratch your head on what the hell is going on. I know I did and feel like the series tries to do way too many things at once.

And inevitably, here are the consequences. Doesn't understand why this main character, why Red Saber, or why anything. Doesn't know why they should invest time in the characters. As stated above in my review, these are not the same people. So any player of the game would be extremely invested to find out WHY Hakuno is still alive after Hakunon died.
This and many other reviews keep providing uninformed opinions from an uneducated perspective of the franchise, by lying and saying they are "fans." This is a problem. You cannot criticize season 2 while at the same time saying you didn't watch season 1.

Conclusion/How you can enjoy this properly

You just have to read the premeditated material. As said before, Extra real sucks. So don't play it. Watch this silent playthrough instead. Put on that 1.5x/2x speed and enjoy yourself. If you feel like you can actually like the combat/the game's structure, then feel free to play it. I could barely find fun in it, but hey, you do you. The "WHAT YOU SHOULD KNOW BEFORE WATCHING LAST ENCORE" videos are really bad. Horrible job at explaining anything. The wiki entries are doable, but you'll have to dedicate a fair amount of your time in order to fully grasp everything. High recommend to the playthrough still.

As for Notes so you can understand what is happening with the outside world/what Overcount 1999 (briefly mentioned in the show) is, you can find the good translation on this Beast's Lair thread. I prefer the image version available for download, as it mimics the original and its setup with the dictionary, but the text version works too. It's also just a damn good read, so I recommend it regardless. It isn't even related to Fate in a sense, in story terms.
You also don't need to play FSN, but I recommend it. I put that there so people don't think I'm one of the mindless drones that sees Saber and has an immediate angry reaction.

Don't play FGO.

9/10. My enjoyment is immeasurable and my day has been relit.

For those of you who've scrolled down and then disliked after seeing the score, you've done a great service in proving my point. Keep them coming.