Part of me wondered "is this a depiction of her mental illness?" before realizing "Duh. You think that a kid who causally treats everybody around her like garbage, hangs out alone, talks about super creepy stuff with the guy under her thumb, and then tried to kill herself on live television wasn't more than a little fucked in the head?"
It really puts stuff in perspective, though. She couldn't stand the rest of society and felt alone until she saw Kasuga sticking his face in Saeki's duds. Seeing somebody be their more honest self when nobody else was looking was what gave her hope. It's even more telling when she sees herself being "consumed" by the darkness that's taken over everyone else, just for it to recede when she saw the same pervert from earlier. She felt afraid of becoming "fake" or "less like herself", like the people around her.
Then we put "But I was also a shit eater" in perspective. Even at the height of her and Takao's madness, she managed to acknowledge that she wasn't really all that different from everyone else; all she did was look the other way while still living "in this town". In that society. It's a good realization, even if her solution to the problem at that time was to kill herself. Once she got some more time to cool down and live in someplace that wasn't Gunma, she seems to have accepted being part of society. She is still alone in the sense that she doesn't seem to have "found love" unlike Takao with Aya or Saeki with her rando, but the final dream showed her interacting with others in the restaurant with an honest but not unkind or disgusted half-smile. She definitely doesn't appear to be regarding them as hideous creatures. She's healed.
The events of Part 1 were just as important for her as they were for Kasuga. Even if it was through blackmail and driving him deeper into corruption, she made her first genuine connection with him. Friends, of sorts, albeit very odd ones. (In fact, it's not very unlikely that she might have viewed him as somebody she was in love with, considering some of her actions and reactions to things involving him. One of the most telling was Saeki's comment that Nakamura was shaking after learning that Saeki and Kasuga had sex. Somebody who was "just a friend" would not have been that upset by learning that.) The strength of their bond seems to culminate in her decision to push him off the stage on the night of the festival. It could not have been a selfish decision. She was about to die, as far as she knew, and had nothing to gain from preventing him from dying alongside her. As such, it had to be for his sake. It could have been repentance for dragging him that deep with her. It could have been an action born from the hope that he might be able to live a happy life. It could have just been that she didn't want him to die. But there's no mistake that the push was for Kasuga's sake, and she did it for his sake because she was the only person she had a genuine connection with. That connection was built throughout the entirety of Part 1, and while she is absent for the majority of Part 2, it was probably that connection that enabled her to better connect with others later. (Considering her mother thanks Kasuga once she learns who he is, even right before she asks him to leave, I think that her mother is also aware of the role he played to enable Nakamura forging her first real connection with another person.)
In the Chapter 1 redux, we see Nakamura feeling disgusted with the society around her, feeling alone in the world, and feeling like what's consuming the world is consuming her. Chapter 1 shows us her witnessing of Kasuga's perversion and the realization that there might "be another like her". We see them become more connected, even if partially toxically so. At the night of the festival, we watch her acknowledge that for all her problems with the world, she wasn't really all that different. At the meeting at the restaurant and then at the beach, we see her considerably more at peace with herself and not actively treating others like garbage - even if she does snap back in response to Kasuga's sudden actions. In her last appearance in the present, we see her clearly relieved that Kasuga is going out with Tokiwa and tell him not to come back "because he's a normal person". She doesn't say this with disgust, but with a sense of bittersweet contentment. The care that she came to feel for him has remained within her and manifested as a wish for him to live as happy of a life as he can, with somebody who has clearly been a positive influence on him. Then in the final vision, we see her living normally, on amicable terms with people around her, clearly loving towards her parents, and - while still walking alone to a degree, because she will always be herself - able to function in society and continue forward.
I think that part of why she also told Kasuga not to come back would be because even if they did become fond of each other, their relationship was basically founded on abuse. So while she welcomed it as a kid who just wanted somebody like her around, she tells him not to come back because she's more aware of how wrong it was and doesn't want him to keep himself in the past. She severs his last ties to the past herself.
If it wasn't obvious by now, Nakamura is easily the most intriguing character in the story to me, even if Kasuga has much better fleshed out development.