on current Plex (as of this weekend) and current Apple TV release (Apple TV 4) and Apple TV beta release (Apple TV 4K) when I pause playback, the video stops and the audio continues to about 1.5-2 seconds. When I resume, the code start with no sound for the same amount of time and the audio kicks in when the video catches up.
This also causes issues if trying to skip forward of back in the stream.
This only happens in Plex, not in any other video app (HBO, Netflix, Hulu, VLC, Viki, etc) and has been happening for several months through several versions of Plex and at least since iOS 14/tvOS 14.
Sometimes (not very often) audio gets out of sync after a pause and the only way to fix it is to exit Plex, force quit it, and relaunch.