Do Music Playlists live in a file somewhere?

Like the subject says, do music playlists live in a file somewhere in the finder?

Here's the backstory:

I've been having issues where my Mac Music won't sync to my other devices, as in any changes made to playlists aren't reflected on other devices, but if I make a change to a playlist on another device, it's reflected on my Mac. It's been documented and Apple Support told me the issue was known and they've been working on a fix (which AFAIK hasn't happened yet).

Today, suddenly every playlist and playlist folder on my Mac Music was duplicated. This duplication wasn't reflected on my other devices, which was odd. When I looked at my duplicated playlists, one version of them would be correct, and the other version would either be empty or have one song. I decided to delete ONLY the empty/near-empty duplicates, and suddenly this deleted EVERY playlist, not just the duplicates, on ALL my devices.

I tried going back a few days in my Time Machine to a Music Library file and restoring that, but that didn't change anything, which is why I'm wondering where playlists might be stored.