I did some different tests and this is what I came up with:
To Start with, I noticed these problems after upgrading Apple TVOS to 16.2 on my Apple TV 4K model A1842 (1st generation). Second of all, these problems only persist on my Sony KD-65XH9077 TV, while setting my Video and Audio to format 4K SDR, 4K HDR and 4K Dolby Vision (all both to 50 Hz and 60 Hz).
But when I set the Video ad Audio to any 1080p format at 60Hz, the files are playing smooth again.
So for now, I’m forced to watch my movies on 1080p, with HDR10…
I hope with this extra information, the issue can be solved.