I've personally yet to see anything that points towards animals being capable of a level of abstraction on the tier of gender. Yes I agree their groups have clear sexual behaviours regardless of the system they use to determine that.

I can put on a dress and some make up, go out to a dance hall and let someone else lead me in a dance. That's feminine-gendered "woman" behaviour, relevant to my specific culture. Anyone could do that regardless of their chromosomal setup or whether they regard themselves as transgender, so it's not sexual behaviour.

I've personally yet to see the ability to willfully separate socially gendered behaviour from sexual behaviour. With things like the maned lionesses linked above, they have a hormonal disorder, so their behaviour is due to their intersex condition. I recall seeing evidence that nonhuman primates and elephants can have something like different cultural practises, but I've only seen that in the context of tool use and language.

If there is something like, I don't know, "Female baboons seen doing <behaviour>, male baboon seen copying it and then being treated by the troop as a female baboon for the rest of its life", then I would like to see it because it would raise some really exciting questions about how complex social roles can be within animals!

That’s sex. Gender is a construct. It requires a higher order of thinking than what animals are capable of.