I'm running Catalina as well, it's not a Big Sur issue.
Look. I'm an IT Professional. I've been troubleshooting hardware and software problems for 30 years. I have narrowed the fault I'm experiencing all the way down to an upgrade of the Apple TV software 2-3 weeks ago (or firmware to be technical about it).
Reading through everyone's posts, there are a lot of common denominators and a lot of differences, but take out all the differences, and it all comes down to the latest software pushed out to Apple TV. Doesn't matter if it's an Apple TV HD or 4K, if you've installed the update then you will have popping and crackling noise and the video will play faster than the audio, getting worse the longer the show plays, when playing from your home library.
The latest latest update (came out a few days ago) has seemed to fix the popping and crackling noise, at least on my Apple TV HD box. Haven't tested it with my 4K box yet, but will do this week. But the audio/visual sync is still a big issue.
The questions I have are: Is Apple aware of this bug? And, do they care as it doesn't seem to impact on their streaming service or other streaming services? Are they intentionally trying to end people having their own home library of films, or not? If they are, then maybe it's not a bug.