Unfortunately the more experienced members stick with our HDR-FOXes like glue! Sorry, haven't got one, can't help other than offer a few suggestions:
If, as you say, when you copy a recording to the drive it shows up and plays correctly, there is obviously no fundamental problem with disk accesses. There should also be no difference between USB ports (except perhaps minor differences in power sourcing capability).
When it comes to listing/playing externally-sourced media files, you need to consider compatibility and DRM (digital rights management). The .mp4 file is a "container format" which multiplexes several different streams (video, audio, alternative audio, subtitles, whatever) into one package, by a specific algorithm unique to the container type. "MP4" says little to nothing about what the video and audio formats are inside the file, what it does say is how they are to be extracted.
Thus, although the FVP-4000T may be able to understand MP4 in general, it may have peeked inside, decided it is incapable of presenting the content, and declined to list the file as an indication the content is incompatible or protected. The same applies to other container formats, eg MKV. There will be other container formats the unit can't understand at all, even if the content is in compatible streams.
On a PC, check the file properties using MediaInfo or something like that. The maximum likelihood of compatibility is if the video and audio streams are a combination of formats used in broadcasting: eg H.264+AAC.
The situation may improve as the FVP-4000T matures. The HDR-FOX firmware went through a number of iterations over several years before Humax got it reasonably OK - see
Things Every... (click) section 1 for a bit of a bug history for HDR-FOX. We built up our encyclopaedic knowledge of the HDR-FOX by investigating, sharing, and documenting information like this; you may find "FVP-4000T video file compatibility" a worthwhile Internet search term.
Whatever, if the unit is not fit for purpose (whether by a fault or by design), you have the option to return it to where you got it from (if the purpose you intend was advertised as being served, or you specifically asked and were assured it would suit).