Apple Music cannot save Music Library file on SSD

I moved my music library from an old HDD to a new SSD, and now when I run Music, it gives me this error every few seconds in a modal dialogue, which prevents me controlling the music app. It has the option for "Do not warn me again", but I don't want to suppress the error, I want to resolve the underlying problem.

The thing that's annoying is that my music library appears to be entirely intact, and all play counts, playlists, etc are all present and correct. I don't want to lose any of that, but I can't see why it would be giving this error message about not being able to find the library file when it evidently can find it.

It also doesn't help that it does not say which file cannot be found, which means I have no way to tell what I should be checking.

If I hold down option on launch it offers to create a new library, but that's not what I want to do. Is there something like a hidden repair option like there is in Photos?

How can I resolve this properly?

[Re-Titled by Moderator]