Tom, in the "Test Clip.mp4" file you made from QuickTime Player, I hear one or two minor "pops" when listening to it in FCP (which sound more like wireless microphone noise). The file info shows a frame rate of 25 fps, not 24.99 fps, which you had mentioned earlier (on Apple's Communities website). I wonder if you had exported the trimmed clip from QT Player rather than just saving it, as exporting would deal with the variable frame rate and transcodes the original file (thus possibly cleaning up the original issue). I don't hear more substantial "noise" like you'd hear from playing a record on a turntable.
I believe the issue originates in the way many applications save video recordings, such as zoom, OBS, and others. They often record and save videos with a variable frame rate, which usually sounds fine in a video player but which can cause issues in an editing application (which can affect how audio is played back).
Perhaps, my suggestion to use QT Player to trim the original file wasn't a good idea.
You could optimize the file when you import it (or afterwards) into FCP. That would help fix things (but as Terry said it creates a ProRes 422 version which may be a storage concern, or not). Compressor would basically do the same thing, giving you a few more options for output file codec, etc.
Shutter Encoder, a free application, can address things on a more granular level. You can re-wrap files, conform frame rate, or just convert the audio, just to name a few of its features. It also has a trim without re-encode function. I wonder if that would work better than QT Player for trimming the source file.
We need a sample file that has the variable frame rate like you mentioned previously...
P.S. - And just to be clear, I really doubt that FCP is creating the issue. FCP is more stringent about proper frame rates when video and audio are linked together (oversimplifying a bit).