There is absolutely no evidence to support the claim that gender transition (in either direction) improves performance. There is ample evidence to support the claim that gender transition inhibits performance.

Incidentally, the Olympic Committee has had rules on transgender athletic participation 1968, ffs. The idea that this is some kind of novel threat to competitive sports is absurd. "Men are participating under a false gender" is an allegation that stretches back two years prior to 1966, after Western media began accusing Soviet athletes of faking gender certification (allegations that were never proven but have persistently circulated in competitions even to the modern day).

As often as not, the accusation of transgender athlete participation skewing the results of competitions has come from chronic underperformers and has been used by Western athletes to defame and discredit athletes from "enemy" nations and from the Global South.

Incidentally, one of the most outspoken anti-trans athletes - Riley Gaines - spent years accepting money from reactionary activist groups to denounce her transgender peers as a personal threat to her safety, while covering up sexual assault by her team's coach for over a decade.