Cool, one pitfall to beware of is that the word "gender" now has 4 distinct meanings (which may contradict one another).
There's the meaning as used in linguistics/grammar, to denote the gender of a word (so, for instance, German has masculine, neuter and feminine word endings and articles - e.g. der, das, die for the word "the" as applied to singular nouns). We can probably ignore this in English (though as a poster noted in connection with an article in a French newspaper, it's leading other countries to get in all sorts of linguistic knots when they talk about tans issues).
As the word has traditionally been used in the social sciences, including feminist theory, it has meant "socially sanctioned, socially policed and culturally acceptable roles, activities, dress etc. pertaining to one biological sex or the other." Hence in Medieval SW England, weaving was a man's job: among the Navajo of what is now California, weaving is/was a woman's job. Soccer in the USA is predominantly a women's sport, football in the UK is predominantly a men's sport.
Trans activists typically use the word "gender" to mean "internal, mental sense of being a woman or a man."
Then, just to really mess things up, in societies which are coy about the sexual act, and by extension the word "sex", "gender" has come to be used as a coy euphemism for biological sex. Hence in the US you have the (to my mind rather bizarre) cultural phenomenon of "gender reveal parties", where the sonographer at the 20 week scan puts the details of the foetus' biological sex in a sealed envelope, which is then given to a cake maker who produces a cake iced in neutral icing. The parents-to-be then throw a party in which they cut this cake in front of family and friends, revealing a blue or pink cake beneath the icing (I told you it was bizarre). IMO, this coy euphemism plays into the hands of those who want to deny biology and use newspeak phrases like "assigned female at birth" when in fact they mean "observed to be female at birth though may decide at a later date they're not happy about this."