add Me to having this issue since upgrading to Big Sur 11.0.1. I cannot mirror my 2019 MBP to my LG UN71 smartTV. This worked before upgrading. My iPhone can still mirror OK. I use this everyday to run zwift. This is really obnoxious. Running beta to Big Sur I lost functionality of being able to be Pair my heart rate monitor, smart trainer, and cadence sensors simultaneously to my MBP and Garmin head unit. I have to choose which I would like to record all of my workout info. Since I’m using Zwift, I have to set it all to go to my MBP. ive been really frustrated ever since upgrading to Big Sur and I am really wishing I hadn’t installed it all now.

Update* On the LG TV, the airplay settings are not in the "settings" menu but in the "Home" app on the LG TV. Once I found this, after a TV firmware update my Airplay had been switched off. After re-enabling airplay on my TV, AirPlay now works. Best of Luck!