Loading Music Library stuck - posted for reference
I have a Macbook Pro late 2013 running Big Sur.
When I tried to sync it with my Apple Music library it simply spun its wheels - even after leaving it running for 24 hours.
No amount of reboots or upgrades had any effect.
Completely signing out from my Apple ID had no effect.
The solution was to close Music, go into Finder ~disk/Users/~username/Music/Music and delete the file Music Library - taking a copy of the file beforehand just in case.
I then rebooted the Macbook and started to sync the Music Library. It took approximately two minutes to sync.
Clearly something was corrupt in the old music library file.