God this manga is so GOOD.
So my take on Rei's speech, I think there's an argument to be made both for Rei being a trans woman and for being non-binary (Neither a man nor a woman, as one commenter put it) but I am leaning heavily towards Rei being a girl. There's been a lot of pull between what Rei wants and what others wanted for her. She was expected to be the heir for her family, one of the most famous in Hyperborea, something only possible if she were male. She also, prior to Eric's explanations of sexuality and gender, had a hard time reconciling her sexuality with her gender, given that it's implied here that she likes both guys and girls. Then most crucially this distance between her and Lloyd that opened up when Rei became female, where Rei said in previous chapters that she stopped seeing him smile. None of these to me feel like she has a desire to be masculine, just that she feels a responsibility to be, like how Lloyd feels a responsibility to marry Rei but clearly isn't romantically interested in her.
On the contrary, everything about this chapter and previous ones indicate her being a woman. Fairly early on after Eric explains what trans people are, Arsenio looks at Rei and muses "The heart of a female, huh?" And a few chapters later Eric admits part of their reason for turning into a woman is to better understand Rei. Now some might balk at using what other characters say to determine Rei's gender identity, but keep in mind its a story written by an author, and everything is put there for a purpose, and I think the purpose here was to prime readers towards viewing Rei as a woman. Then more crucially is all of what's shown on this chapter. Playing bride, wanting to wear her sisters' pretty clothes (which has been mentioned before this chapter too), living as a woman in that flash back and being happy doing so, and most crucially wanting to stay a girl so badly that other spells could not successfully turn her back. These all scream a desire to be female, and I think her line after that is more in reference to not wanting to be seen as a different person now that she's a woman, the way Lloyd had done when they were younger. Rei is Rei, same as before even though she's a girl.