I think your take is reductive. Gender isn’t about stereotypes. I’m sure that for many trans people, part of their trans discovery was not feeling like a stereotypical member of their sex, but there’s more to it than that. You can say that gender relates to a lot of things. Gender is ultimately an internal experience that means different things to different people, and isn’t necessarily related to identifying or not identifying with any given stereotype.

Bioessentialism in turn reduces people to genitals, and sort of refuses to address intersex people because something something “outliers don’t count”. At best it says sure, you can dress up however you want, but it’s super important that everyone know What You Really Are so they can put you in a box and appropriately segregate society.