M0nica
There is a very simple solution. Set up parallel sports teams/leagues/ groups for transpeople.
Professional football was once men only. Now we have women's team's and men's teams, women and mens leagues, each with its panolpy of cups and awards. All that is needed now is trans teams, trans, leagues, and cups etc - and the same in every other sport.
I really don't think that's what they want, but of course they're free to do that and lobby for official recognition just as the women did. I've said before a German (I think) swimming event set up a few races for transgender entrants. They didn't get one single application. Transmen haven't competed against men because their times, distances etc don't come near, and they'd never get selected for team events. Transwomen want the validation and advantage they enjoy against women in sports. It's notable that successful transwomen competitors were never successful when they competed in their own sex class. Lia Thomas as mentioned by Carlotta as a prime example. I can't recall one successful elite sportsman that has transgendered to a transwoman while still competing. Caitlyn Jenner formally Bruce has become a transwoman but not when he was a gold medal winning decathlete.