I wonder if wide angle and/or 360 degree cameras like the one discussed here could make sense to capture your own skating programs, without having to worry about skating out of frame:
https://www.avsforum.com/threads/insta360-x4-action-cam-review-a-full-circle-of-fun.3306652
https://store.insta360.com/product/x4
BTW, I've not used that camera, or any similar camera. And it isn't cheap. And more expensive if you buy the accessories.
Are there cheaper alternatives?
(Of course, for individual skating routines, it might theoretically make more sense to have a camera track your location, and cameras that can do that exist.) But making that work might sometimes be complicated, and may not work at all for dance, pairs and synchro, when those involved aren't close together.