I don't think Kanae considers herself trans, it seems like she wanted to take the place of her late brothers as the head of the household. Maybe only men could carry that titel?
Honestly I initially thought she was a girl bc of her appearance but mostly her name. Kanae is def more common as a women's name. But yeah many ambiguous cases here so didn't question her being a guy later on.
Btw that last panel with the excerpt from Takatsuki Sen's book was v creepy.