It would seem that my Music woes weren't over after finally cutting the cord to my Apple Music subscription and iCloud Music Library.
While hunting for duplicate tracks to remove, it became apparent that there were a lot of dead tracks in my library — in other words, tracks without a file attached to them.
Eventually I decided to bite the bullet, delete the Music library file in Finder on my Mac, then re-import my music library. In the process I lost all my playlists, but regained a load of tracks that I'd assumed lost.
I doubt that the mis-management of my library happened all at once, but rather slowly over a number of years, through both iTunes's and now Music's stewardship.
I would dearly love to switch to another music player/manager, but most of the alternatives out there haven't been updated in a while and so aren't future-proof.
I have a feeling that Apple haven't designed Music to handle libraries as big as mine — currently over 50,000 tracks and 600GB — or have just stopped doing any testing on that side of the app, preferring to focus on the subscription and synching instead.