It's sad that I posted this one month ago and there still aren't any solutions. I'm hoping the Apple developers can come up with some sort of solution since tech support was not able to resolve the issue. At the very least, it's helpful to know I'm not the only one having the issue. I also reset my Apple TV to it's factory settings, which did not resolve the issue. I will make sure to post an update if anything comes up.

I was initially excited that my laptop upgraded to a new version of Big Sur. I then checked both Apple TVs to make sure the are up to date (which they are). Unfortunately, I am having the same exact issue as before. The AirPlay issue is still not present on my MacBook Pro. Instead it is just Screen Mirroring, which doesn't even work. As stated before, my iPhone continues to work just fine with AirPlay. I really hope Apple can fix this soon because it has been a long time and these devices are supposed to work pretty seamlessly together.