same problem here. only left or right airpod pro works on latest big sur 10.0.11 or latest iOs

also happens with official big sur release macOS 11.0.1 (20B29). one of the airpods connects and plays sound for 3-5 seconds than disconnects... also the battery status shows 0% for the airpod that is not playing. if i disconnetct the airpods, put in the airpod that has shown 0% and didn't work before and connect again it starts playing and the other one shows 0% battery.... so... both work and can play music. it doesn't seem like this is a problem with hardware. also while playing music with one airpod the sound is flickering. there is no way to use this airpods right now.