There have been various messages about problems accessing music libraries on macOS Monterey. I had the same problem but have managed to get it working again.

The problem on my system was linked to the way the library is indexed on macOS by a daemon that is installed by the macOS Sonos App when you use Preferences to setup a shared folder. The daemon in installed here /Library/Application Support/Sonos/SonosLibraryServer. The bug comes from the SonosLibraryServer not having permission to scan the disk. You need to add it using System Preferences → Security & Privacy → Privacy(tab) → Full Disk Access.

It's possible that a new install of the Sonos App will handle this correctly, but I already had Sonos App installed from a previous macOS version.

After giving this permission, the music library is indexed as normal and can be played across the system. This SonosLibraryServer also seems to handle the file sharing aspects too, making a specific definition for the music library unnecessary in System Preferences → Sharing → File Sharing

Hope that this helps some of you!