I swear there was at least one more server I looked at but passed over and I cannot recall the name.

Maybe Jellyfin? It’s best at movies/shows but it also handles music (and more). The native music experience isn’t great but it works. For Windows/Linux/Mac you can use Feishin (I use and mostly recommend it, also you can use the web app version). Android has Symfonium I use and highly recommend it, also it works with FAR more than just Jellyfin). I don’t use iOS but I just looked for an iOS app and found AmpFin (not to be confused with Finamp).

You said your users have their own libraries. Jellyfin works great with this. Out each in its own folder, create a new library for each in Jellyfin (pointing to each folder), and you can choose which accounts can see which libraries (and optionally let them manage libraries too so they can delete songs or modify metadata for the libraries they have access to).

I’m a fan of Jellyfin if you couldn’t tell…