There have definitely been women who take the role of men both in history and currently but it's almost always more about survival in a highly patriarchal society; women who wanted to attain certain professions or roles that were considered "only for men".

I agree about the other cultures' "third genders" basically always just being HSTS. India's hijra, Thailand's kathoey(ladyboys), the Muxes in Mexico (and iirc that was only one small portion of Mexico, not the whole country), they're always just HSTS. From a biological perspective, society can "afford" to have men not play the male role in reproduction (hell, the men who do want to reproduce would probably prefer it that way), but women are basically never "allowed" to opt out of being seen as the baby makers.

ALSO, the cultures that have "third gender" are typically the MORE patriarchal ones, because they have a stricter (heteronormative) definition of how "men" are "supposed" to act and as such men who don't act that way are labeled "non men". It's both (a) not progressive at all and (b) not the same thing as trans in Western culture, because trans in Western culture demand to be considered literally the sex they identify as, whereas the whole point of third genders was letting them be a third thing.
Basically my rebuttal to those "wow muh noble savage much enlightened non western cultures have third genders!" arguments is "Yeah, other cultures have a word that means 'f#ggot' or 's#ssy'. It's not that progressive, nor does it make trans women literally women".