*EDIT* Misread initial post as I don’t use Apple TV app for anything other than the apps that sync in with it such as Amazon, Disney+, etc. I use Plex mainly for watching anything I haven’t purchased as digital media & ripped from my own personal original Blu-ray/DVD collection (Other than one offs that I might have on a USB-C thumb drive to not mess up the index on Plex)
No issues with my 2018 iPad Pro on 13.4.1 with playing back ANY video thru any app. Ripped MKV/MP4 video plays fine off of USB stick via Files or Readdle Documents, as it does from my Plex servers in my loft over the network in the Plex app. Amazon Video, Vimeo, YouTube, Netflix, Disney+, Apple TV+ (for iTunes purchased video including 4K), etc are all fine as well. The only issue with video apps that I have had since buying the iPad Pro a couple of months back is with the ITV Player app that wouldn’t go past a grey screen until last night (ITV must have done something to resolve it at their end as nothing changed here & now works again).
Can’t offer anything other than what has already been mentioned but like most of the issues that get reported on here, some people may be affected & others aren’t with same hardware, software, etc & no real reason to why the problem exists!