Okay…I see your point. In real life, though, this rarely seems to happen. When a biological male actually does this then let’s look at it. I believe at this point the IOC rules would not allow James to compete.If Jaya identified as a woman would Jaye be a woman?
In answer to your questions, though, if James identified as a woman but in all other aspects was a man then I would still address her as a woman (eg.using her prefeferred pronouns) out of respect to her wishes but would otherwise say she is not eligible to compete in the women’s division.
In other words, I think that how an athlete identifies (ie. male vs female) should be one but not the only criteria considered in these decisions.