Op I totally understand what you want for your daughter - I do think what you’ve tried has been pretty limited in a certain type of organized sport box (though I understand you’ve offered other sports like cheer) but I agree with others that I would really try other things now: art (100% if shes shown interest! Ceramics, photography, so many cool things), any interest at all in biking or running? Sometimes these can be good fits for kids who don’t like the pressure that can come with team sports. A friends son LOVES cyclocross because he gets the fun competing with others team feel but only actually has to “compete” with himself, no one else is depending on him. Probably not for your daughter and also, it doesn’t all have to be a competitive thing - just biking as a family can provide so much joy. There are regular groups in the area that meet and mountain bike that are so much fun, if you have any interest for example (with kids, called Smores) non competitive, great way to learn, individual, great for my kid with adhd. If she shows any interest in running and you’re in Arlington or look for one in your area:
https://runsignup.com/Race/VA/Arlington/HealthyKidsRunningSeriesArlingtonVA
I’m going to throw out some other random things: saw this the other day, so different but for the right kid could become a passion:
https://www.hisawyer.com/art-house-seven/schedules/activity-set/1550541?source=semesters
Theater. I know you want something active - stay active as a family, get biking, hiking, outdoors, and she’ll be ok. Consider things like track in middle and high school. And the passions may lie outside of sports and that’s ok.
Also - consider an all girls sleepaway camp that runs for 3-4 weeks. I may sound crazy to some but it’s a GREAT spot for girls who aren’t spending their summer on travel sports and crazy focused on one thing. They build so much confidence, try new things. In VA there is camp Carysbrook and camp Mont Shenandoah that both have these vibes.