Small update: thanks all for the helpful hints and ideas.
I finally gave up waiting for Photos to auto-tag anything, upgraded my iCloud account, and turned iCloud Photo Library on, only to then re-download it all to a new library, as there apparently is no other way of salvaging a Photos library that may or may not be broken (who knows).
However, now even uploading to freaking paid iCloud has been stuck at some random image, with no warning, hint, explanation or feedback of any kind, whatsoever, anywhere, at all.
So now I finally give up on all this pretentious Apple ****, and am in the process of switching to Google Photos, and later to Android. It's been a good 30-years run with Apple, but somehow I feel we're not on the same page anymore.