After I read this, I had to reread the final chapter to make sure of something. That something being whether Shizuku still loving Kaori and proposing to her grave at all contradicted Kaori’s wishes.
Having reread the chapter, I wouldn’t say they do, but I also wouldn’t say Shizuku is being healthy about this.
It having been five years, I don’t think Shizuku should be holding onto Kaori this close, however I should acknowledge that people grieve at their own speeds, so my point does lie moot there.
Even putting aside for a moment the question of whether or not five years is really all that long (it kind of is, especially at such a young age and for such a brief relationship, but it also kind of isn't, especially when you've got this kind of romantic trauma hanging over you), moving on from losing a lover doesn't have to mean finding a new lover. It means finding a way to live a happy life without the one you lost instead of wallowing in that despair.
With that in mind, I think Shizuku is doing well. Not perfectly, perhaps, but she's come out of her shell, she's found something that she thinks she wants to do with her life, she's got a reliable support network built around the shared love and loss of Kaori, and the love she still feels for Kaori is a source of happiness and inspiration and not something on which she's harmfully fixating. I see the proposal as being less a matter of "I want to marry this dead girl" and more a matter of tying up a loose end by doing something she wanted to do while Kaori was alive but wasn't able to, making "I would have married you" something more concrete than just a thought she kept bottled up. Rather than stagnating and holding on to Kaori, I think that's a part of the process of moving on, closing the book on one of the things she regretted not getting a chance to do.
Will she find somebody new to love? It's hard to say. I think her chances are relatively slim, being somebody who will almost certainly always be a little socially awkward and that making it hard to meet and fall in love with people, but I don't get the impression that she's closed herself off to being happy with somebody else. She just doesn't feel the need to look for a new love yet, and that's fine, so long as she's still living life fully and healthily.