Hi,
I've managed to resolve this issue. Had extensive help from Apple (through chat and a few calls - quite pleased with the service I got) and eventually I came across something that worked.
My setup is a large music library (65k) on a NAS. IMac on Catalina 10.15.7 and an Apple Music subscription. We tried everything from test accounts, re-installs, etc. I could get it to play on a test user account (where it only showed the cloud versions of my music) and it also worked on my real login account when signing out of Apple (and playing local files only).
I noticed that the library file, so the file called Music Library typically located in your music folder on your iMac (in <username>/Music/Music), was very large for my real account was way bigger than the one for my test account even though they contain the same amount of songs. It is about 30 times larger (900Mb vs 30 Mb). As I also had a slow Music app, especially when a new song starts (app becomes unresponsive for a while), I tried to copy the Music Library file from the test account into the music file of my real account just to see what happened. I left the old one in the same folder but renamed that one first before copying in the one from my test account. In the process I also reset the default media folder within Apple Music to default (it was set to point to my NAS music folder before). Not quite sure if this did something, though.
All in all, when I did this and restarted Apple Music, it started updating the cloud library, but the funny thing is: from that point on Music didn't crash anymore! I was expecting Apple to pick up the new library file. Instead, I noticed that it was still using the old and renamed music file (I could see it being modified everytime a song finishes). Turned out that the new music library file was not being used. The old one is apparently connected to the application in other ways than just the filename :-).
It took my computer several hours to update the cloud library but as said, Music hasn't crashed since.
Hope this makes sense :-). Feels a bit like a lucky thing but maybe the resetting of the cloud library after renaming it did the trick for me. Curious to hear if this worked for you.