I don’t remember (sorry) but has your daughter been evaluated for autism?
Some of the things you describe fit. But having read the list of characteristics, I’d personally be surprised if every single person I’ve ever met in my entire life did not fit into the spectrum—
And it doesn’t matter much anyway. What matters is developing strategies and helping her to develope strategies for coping when things do not work the way she/ the world needs.
Does she dislike the actual physical aspects of writing? Pen/pencil and paper? Keyboards? Would switching whichever she uses help? Does she like to draw? Does she like word play? Rhymes, puns?
My understanding is that more and more kids are leaning hard into graphic novels.
A couple of suggestions: Calvin and Hobbes. Poetry. Seeing if she will engage in pen/paper games such as tic tac toe or hangman. Leaving her notes that ask her to respond in some at such as yes/no, in the beginning and going on from there. Word games in general.
Or if she says something that you notice as being particularly funny or wise or interesting, etc, saying you’d like to write that down so you can remember it.
Or starting a story ( orally at first if needed) and she must pick up the thread: what happens next?
If you haven’t heard of these before, may I suggest Junior Great Books? It’s a series of books of short stories that are very well written and lend themselves to open ended questions that build on interpretation of events and what might come next. Lots of Why’s? I used to volunteer in the program with my kids’ elementary school. An example that I remember is reading Jack and The Bean Stalk. One of the questions at the end of the story is: Why does Jack go back up the stalk the third time?
Lends itself to discussion and multiple answers that can be written in a sentence or two.
https://www.greatbooks.org/k-5-materials/
I’d recommend Shel Silverstein but I absolutely hate and detest The Giving Tree.