So my comment about new categories should be understood to be within the context of "trans women are women, full stop." We have different weight classes for men in wrestling, but no one would question that the featherweight champion is a man, or that the heavyweight champion is a man, even though a heavyweight would clearly defeat a featherweight every time if they were to compete against each other.

This is why there is so much acrimony on our side. It appears that even for our allies, it’s fine for us to compete, so long as we don’t win.

That definitely seems unfair and I don't ascribe to this. There's generally nothing wrong with a trans women winning a sports competition when competing against other women (who may also be cis or trans).

The whole argument from the other side centers on the assumption that men obviously are better than women at sports just because, and thus it's obviously unfair that ...

Except that cis women have beaten cis men in sports before, see https://www.elle.com/culture/g30119/female-athletes-who-won-against-men/

In some sports women generally do better than men, see https://www.bbc.com/future/article/20240731-the-sports-where-women-outperform-men

So the central premise that the other side tries to bring is faulty to begin with.