This situation is commonly seen, and it has nothing to do with FCP. In general, "smart" TVs have fairly weak CPUs relative to a laptop, and have highly-specific requirements about what video file characteristics they will accept.
More is involved than volume format of the thumb drive, and more is involved than a simple high-level spec like H.264 or HEVC. Typical "smart" TVs often require a very specific range of characteristics such as GOP length, bitrate, bit depth, container type, etc. Without knowing these specific requirements, it's easily possible to produce a video file that still doesn't play properly on the TV.
Check the manual and any manufacturer info about specifications required for playback of 4k video files.
If the manual lacks sufficient information, you will have to contact the manufacturer about their detailed video file criteria for smooth 4 K video file playback. We need highly specific information here.
A laptop or desktop or even an iPhone have vastly more powerful CPUs than a smart TV and can handle a wide range of encoding formats. It's possible your TV is optimized for a narrow range of codecs or requires specific encoding criteria.
Tell your TV manufacturer or support channel for that TV that you need detailed technical specs for the playback requirements of video files on USB. That includes codec, resolution, color space, bit rate, frame rate, bit depth, chroma subsampling, container type (e.g, MP4, Quicktime, etc). Given that info, it is likely possible to produce a compatible video file using either FCP, Compressor, or other third-party utilities such as ShutterEncoder or Handbrake.