Are trans people ever more likely to fit the opposite sex stereotype? Usually their gendered behavioural trends totally undermine their self-identification.

Good question. A lot of natal male TRAs display male socialization when it comes to sex, hence you see jokes from the worst ones about "raping TERFs with their girldicks." But then there seem to be a segment who believe that sexual submissiveness makes one female, or that sexual submissiveness is the definition of being female. And some of them seem to have been inspired to transition from "sissy porn.' So they claim to be these submissive feminine beings, but their overall socialization is still full of male entitlement. Of course I'm not talking about all trans women here. But it's a noticeable feature of some, especially those who decide to identify as lesbian women.

It's only during copulation that the female is sexually submissive

Really not even then if you define submissiveness as a mindset rather than physical receptivity. And of course pointing to animals is a double-edged sword because we're not bees or clownfish or anything other than human, but hyenas are an interesting case. They're quite female dominant in all areas of life, including sex.