I will give my thoughts about it and try to only stay in Nadeko Draw ( so it will not be really long ) and not write about what happened before. There will be some interpretation and honestly I’m just writing what comes to my mind.
So this arc makes me sentimental, the amount of emotion and the retrospection of it is absolutely fabulous.
Nadeko comes to terms with her past, finding the courage to move forward. Her journey in this arc was impressive.

Nadeko, facing herself, facing clone trying to kill yourself. Is it not terrifying ?

Nadeko, locked into her room, since the incident with Kaiki and Araragi, is drawing, drawing to improve herself to be a mangaka but ultimately reality came back to her when her parents scold her : “Stop wasting time on stupid things like this. Go get a job once you finish middle school.”. She became friends with Yotsugi who had the idea of creating copies of Nadeko to help Nadeko become a mangaka. Gentle Nadeko, Fawning Nadeko, Anti-Nadeko and Divine Nadeko. Basically she confronts all of her parts, all of past selves, but they are still her. She understands them and accepts everything from them and comes to terms with it.
I will talk about Araragi, Shinobu, Hitagi and her. At first I feel like she wanted to erase Araragi from her life, making it seem like he never existed in the first place ( she never mentioned his name in all the arc ). But I thought that it can’t really be this because she wants to know and understand Hitagi and Shinobu better and they are both extremely related to Araragi, so she will be bound to meet him again eventually. So here is what I think. She just wants some time to think about it, to heal her wounds and get the courage ( she is still shy, it’s Nadeko ) to face him. She is just taking distance until the time comes when she is ready to face him and not running away. And for Shinobu and Hitagi. She wants to know them better, she is opening herself to the people she never thought about in the first place ( they barely spoke, just trying to kill each other ). When she will get their feelings and who they really are, she will be able to ask forgiveness and say sorry and of course to forgive her past selves too. Because let's not forget that she tried to kill people who, in a way, saved her ( Hitagi when she deceived Nadeko with Kaiki and Shinobu who pinpoint her cuteness and the way she is living is wrong and Nadeko did not forget about that ) . So she is not really trying to erase Araragi ( I thought about this at first because she never says his name in the entire arc and I will give my thoughts about this later ), she just needs more courage to face him.
It’s really hard to think about Nadeko. I always tend to think that she is and will be a victim. But in Nadeko Draw, she is trying to free herself from being a victim and ultimately not to forget him, but to free herself from this bond that chains her ( she has done it in Nadeko Draw ). And we get to their parents. At first I was like, where did they go ? We never heard of them after the incident since what they say to Nadeko. So here is my thought. They are not important for the future of Nadeko. By that I mean, just when Nadeko stopped acting cute and the way she did, they came and told her to stop drawing ( as if there was an anomaly in the character whereas she is just evolving ). But Nadeko changed, she will stop being the victim and she will stick to her dream. So if their parents don't try to understand her daughter, what is the point ? They don’t try to understand Nadeko’s feelings at all. They just want Nadeko to act cute and not be bad. But maybe like Sodachi is saying, maybe they are making this up, saying harsh words to convince Nadeko, but ultimately they don’t try to understand her. So she is living, sure, she may never get approval from her parents but « It's alright, Nadeko-chan. You can fret about your future all you want, but as long as you keep on living, you'll grow into adulthood. So don't you worry. ».
And that’s what is living, you will make mistakes, you will have to interact with the world and ultimately your mistakes can be considered bad to someone but that’s not a problem, when you grow up your learn, she will learn from her mistakes and solve them for a better future. So as Nadeko is growing up she can’t let her parents chained her down again by the image they put into her.
For why she never said Araragi's name in the entire arc. Araragi is someone who will save everyone without distinction and he will not hesitate even if his life is in danger. So not saying his name, means Araragi will not get involved in Nadeko’s problem, she will be able to let go of the embodiment of a victim ( as she will not be saved by him ) because she will save herself. And that’s why I love Nadeko too. She saved herself and she will stop being blind by her love for Araragi. Her peak was just phenomenal : she is talking to herself « I will never disappoint you, I will never forget the feeling of happiness I get from waiting, from thinking about them. I will never let your lost love be in vain. I will pursue my dreams, I will not learn, and I will keep falling in love. I will remind myself that I don't want anything else. » I almost cried here, no joke ( I was having Owari OST, when Araragi saved himself .) This moment is also a message to him : I will not let you interfere with my life, I will move forward, and live my future in the way I want. And for this, all she needs is to face him one more time to ask forgiveness. To make a beginning of her future ( that has already started because she found a new job with Gaen ) and find a new love that will make her smile.

Nadeko is growing up. She is letting go of the persona that everyone put into her, like a puppet, the shy little girl. She is letting go of this fake mask and she knows that it will not be easy because everyone « loved her » but it was just a facade too, as they absolutely get no interested of who she was. But now she is showing off, (starting to and her hair is really short ). She will : « I will never shirk from hard work or escape from crowds. » She will face people and not hide behind a facet that the society and the normalcy of it put into her. She will become a mangaka and break the false laws that society puts into her. She is completely stepping out of her control zone and there will be a lot of uncertainty because of course as it is hard to know if the choices we made are right for the future we seek. But her story will not end yet, there is more, the choice to believe in a future filled with happiness. Even if her main story is finished, she will have to find courage to live on to the future that awaits her, because life continues on and what awaits her, happiness or something else, depends on her.
What I find impressive too is that, when she became a Snake, she never heal herself or her wounds ( thanks to someone I learned that snake represent healing ) but now, without being a Snake, she heals herself, by being herself, a little girl who love drawing manga and want to be a mangaka, she is able to heal herself. In Nadeko Draw, she faces the part of herself, she is embarrassed, is scared and feels guilty about them and even it is painful, recalling back all the mistakes. But in some way, she is jealous and she envies them. We see she got power, power to express her feelings, she drew herselves, and they were able to express themselves. She is able to show her « unseen » part of her by bringing them to life and she express her feelings with her talents of drawing to help herself ( literally the opposite before Nadeko Draw ). She even got a job thanks to her passion.

Sengoku Nadeko, be authentic to yourself, be whoever you want and do not be scared of crowd, be authentic to yourself and do not go back on hiding behind a mask, continuing on this road and taking the happiness with a new love, the past is behind your back, the future and today is another day. These other Nadeko’s were real, were you, and you acknowledge them even though they were not a permanent part of you, it is meaningful, because it is still a part of you and as life goes on. Cherish your past and embrace the present and everything that will make you happy.