Library won't open and/or update/save (Music app - local library on Mac - NOT ABOUT STREAMING)

Firstly, to avoid confusion, this has absolutely nothing to do with a subscription to Apple Music or streaming from that service. I do not subscribe and I do not stream. This is purely about my local music library and the Music app on my Mac Mini (late-2014), although it may also be a Big Sur issue.

[Sidebar: I hate that Apple has made every software name so utterly generic that it's almost impossible to ask a question without causing misunderstandings and confusion.]

Here are the problems I'm having:

Ever since updating to macOS Big Sur (11.4), the Music app has been a nightmare and pretty much just won't work:

The app rarely opens and loads my library successfully - it goes into a never-ending "Loading Music Library..." status window. I've literally left it for more than a week in case for some reason it feels like it has to reexamine my library in order to load it, but it still never gets anywhere. Trying to quit the app doesn't work - it still can't exit that "Loading Music Library..." status window. The app is still theoretically working - going into Force Quit Applications doesn't show Music as "not responding," but forcing quit is the only way to get out of the app.

On the rare, rare occasions when my library miraculously loads (we're talking one in 10-15 tries, multiple restarts, etc.), I can play songs, add albums, etc., as usual, and the song list and playcounts will update in the app as you'd expect. But the next time I manage to successfully open the app, all updates from the previous session will have disappeared, and the library will be back to its older version. Even though the files from newly ripped albums will show in a finder window of my local library location (indicating that they were imported successfully), they do not show up in the Music app window once it's reopened. This is likely because of the next item...

When trying to quit the Music app (if it was successfully opened), it will go into a never-ending "Saving Music Library..." status window. As with the first problem above, the app is theoretically still working, but it cannot get out of this progress window. The only way to get out of the app is to force quit again - which is likely why the library never retains new playcounts, etc. - it can't seem to save the music library in its updated state.

While Music was caught in one of its never-ending status windows, I opened Music preferences to confirm my library location, and discovered that for some reason, the library location was completely blank. Aha!, I thought - this must be the answer! I directed preferences to the correct library location, closed the window, and... nothing changed. I went to the preferences window again, and the library location was again blank.

FYI, the TV app has identical issues. My iPhone has similar issues showing up in a finder window when connected - the system registers that the phone is connected (it shows in the finder sidebar and main window), but I just get the spinning progress wheel and it rarely actually connects and shows up in the window so that it can be synced or backed up locally.

Some important notes:

• Yes, I have tried restarting the computer many times.
• All my OS software and apps are up to date and are on the current official versions (no older versions or betas).
• My local music library is hosted on my Synology NAS. This has been the case for years with no significant problems. The NAS is constantly mounted and all files are accessible via Finder without issue.
• My local music library will not show up on my AppleTV units, either. But it continues to show up in Plex with no problems (including the recently added files that won't "take" in my Music library).
• In Mac Preferences>Sharing, I've discovered that when I highlight Media Sharing it doesn't show me a description the way all the other line items do (File Sharing, Printer Sharing, etc.). It also will not allow me to check the Media Sharing box.

Anyone have any ideas? This has been intensely frustrating, and based on the Media Sharing issues noted above, there may be something more going on than just an issue with the Music app.