that kind if stuff depends on the individual. most are well aware that they are in a human body and don’t have the abilities of their kintype, but can take on behaviours that feel familiar. like a dragonkin might hoard things or have collections of things. coming to understand a person’s otherkin identity is typically a religious thing. again, it’s not connected to gender at all, but discovering the identity is similar to discovering gender- with the feeling that, while physically one thing, it doesn’t feel correct.
most people are fine with their human bodies, I haven’t met any kinfolk who want. like their concours need implanted into an animal or anything, but a lot of us feel more comfortable when our clothing if fashion sense kind of reflects our kintype?? if that makes sense. like batkin wearing clothes with bats on them or plants wearing flower crowns.