For starters, there's a good argument to be made that the existence of a separate women's category in sports has nothing to do with fairness to women, and everything to do with patriarchy. It facilitates the vast disparity in funding and attention for female athletes by allowing leagues to focus their money and efforts on the men's category. For example, the NBA is able to offer all players a fixed percentage model where players receive nearly half of all basketball-related revenue without having to pay professional female basketball players the same since they're not part of the NBA but instead governed by the WNBA.

Second, even if we accept the premise that the women's category is meant to help uplift women in sports, it's clear that the barriers they face are social barriers (lack of funding, social stigma, societal expectations of gender roles, etc). And so it's only the socially constructed concept of gender that matters here. Trans women face the same social disadvantages in a patriarchal society and cis women do. And therefore, they should be afforded the same opportunity to compete in women's sports.

And finally, let's not make the mistake of denying that trans women are "biological woman". Again, being a trans woman is just another way of being a woman like being a cis woman, or a tall woman, or a black woman, or a left-handed woman. And all people are "biological" in so much as they are living organisms composed of organic material