What application would work to edit mp4 video files on Catalina/

Don't know why, but some apps will only pay attention to specific file extensions. So, even though .mp4 and .m4v are really the same thing, one works, but not the other. The only actual difference between the two is .m4v files can be protected with DRM copy protection.

To test, just rename your .mp4 file with a .m4v extension and see if iMovie will open that.

If importing into iMovie doesn't work, you can try using Handbrake to encode them in a different format that iMovie will import.

I just tested a .mov file (MPEG-4 codec) that wouldn't import into iMovie.

I used Preset "Fast 1080p30" to encode the video and the result imported into iMovie.

What preset did you use?

Apple Intermediate Codec has been dead for years. No need for it as the systems can process the edits fast enough with a production codec.

Did handbrake not recognize the codec used. What codec was used?

Photos has some capability to Import video, then export in a codec iMovie can import.

MP4 isn’t a codec. It’s just a wrapper.

H.264 should have been importable int iMovie.