① If you use a tagging application, then do not mark it as ‘4K’. Leave out this tag for this resolution instead. The Computers app won’t see files tagged as ‘4K’, even though 3840×2160 is supported for the Apple TV 4K models.

② Files with certain audio formats may also be problematic, if different than what the device natively supports.
Apple TV doesn’t support DTS audio or its variants.
Apple TV doesn’t support Dolby TrueHD, nor Dolby Atmos as substream in Dolby TrueHD [like Blu-ray].
Apple TV 4K does support Dolby Atmos as substream in Dolby Digital Plus (E-AC3+Atmos) [like streaming].
③ Video in files should have the proper profile and level to mark support for that hardware model.
Apple TV 4K (1st generation) technical specifications - Apple Support
Apple TV 4K (2nd generation) technical specifications - Apple Support
Apple TV 4K (3rd generation) technical specifications - Apple Support
SDR: Main profile, up to Level 5.1, Main tier (3840×2160@60Hz)
Dolby Vision: Profile 5 up to Level 9 (different scale), Main tier (3840×2160@60Hz)
HDR10: Main 10 profile, up to Level 5.1, Main tier (3840×2160@60Hz)
HDR10+: Main 10 profile, up to Level 5.1, Main tier (3840×2160@60Hz) [A2737 and A2843 only, but backwards compatible as plain HDR10]
High tier files may have bitrates that exceed the processing limits.