After I sent that message, I realized it was not fair for me to ask you to provide sources I could easily look up myself, so I just looked a few up myself and found some similar results as you did. Overall the data is still lacking or incomplete, and you also see studies like this...
https://pmc.ncbi.nlm.nih.gov/articles/PMC7846503/
https://pmc.ncbi.nlm.nih.gov/articles/PMC9331831/
Perhaps the NIH (ncbi) has an agenda? It's been over a decade since I got my BA in neuroscience, but I can see the value of both arguments. I'm sure your qualifications to speak on this are just as high, if not higher than mine.
I get that my logic is not perfect, and I don't think we should be pandering to the neonazis or the neoliberals. The wisest solution is not always the most logical, however, and we must pick our battles - new ones every few years. We need pragmatic legislation that helps everyone, before we start to address niche difficult issues like transgender equality in sports.
For now, I still think a bandaid solution is best; Trans women of any age cannot compete with cis women unless it's expressly allowed by the regulatory committee of that particular sport - i.e. in an open division or in a sport where physical traits are not a statistical predictor of success.
That would help liberals and republicans get off this merry-go-round of absurd hypotheticals and focus on the major issues happening now, affecting us all.