my issue isn't with airplay, it works. my MacBook Air 2012 with latest Catalina airplays and shows my display in full 1080p resolution, and native resolution of my Samsung tv is 1920x1080, and Apple TV is set correctly, using full resolution. now, my m1 MacBook Air, Big Sur, when airplaying from this machine, display in settings shows only 1280x720. something in this os, I'm inclined to say it's software, is not allowing my display's full resolution of 1920x1080 when used as a separate screen for screen mirroring/airplay. the setting isn't even available in Big Sur's display settings, when choosing 'scaled' rather than 'default for display', it only shows 1280x720, and no other choices, and Big Sur thinks it's the display default, since they're the same either way. once I switch back to my old MacBook, and airplay with that, I get the full 1080p resolution. so, Apple TV is not at fault. the television is not at fault. it's my m1 MacBook Air, and Big Sur, that's the problem. bump this up to the Big Sur programmers to fix this.
additional information: when selecting the color tab for that display (my appletv 4k and Samsung tv), I see display profile HD 709-A. no other profiles are available.