First point, no Bruce, 'biological woman' is not a technical term, it is a worthless one. Just don't use it, its only purpose is to be transphobic. The terms cis woman, cis man, trans woman or trans man are more useful, give more information. If you continue to use 'biological male' or 'biological female' or any term like it, you're choosing to be transphobic and/or unclear. And no, the exceptions demonstrate that the ability to give birth is absolutely not the physiological difference between men and women.
TL;DR just stop calling people 'biological men' or 'biological women', it's a worthless term that serves only to play into the hands of hateful bigots.
I think at almost every level, we don't need to care about someone's testosterone levels. The overwhelming majority of trans athletes are not trying to steal gold medals from cis athletes at the Olympics or whatever the narrative is, they're just trying to play social sportsball at the lowest community level. I've played a lot of team sport at that kind of low level, and not once have I thought the competition would be improved by having me or my fellow athletes tested to see if they're juicing. The top end professional level is frequently used as the justification for treating trans people like trash, but the implementation seems to be aimed at all levels. I think it's reasonable, specifically at those top levels of competition, for trans women to have done a certain amount of HRT before competing (as is almost always the case) but I don't have much interest in applying this to athletes with various intersex conditions, any more than I think we should penalise taller athletes for being taller, etc.