Is there a limit of the # of songs in the “Music” app on an iMac if you are not synching with the streaming Apple Music service?

The size of your Music library should only be limited by available storage. Obviously the larger the library the longer it will take to update when you make changes. The 100,000 song limit applies to the Apple Music subscription service, and excludes your unhidden music purchases in that count. If you exceed it you can still add tracks to the library, but the library won't be able to sync to your iCloud Music Library, which is what other devices and computers see when Sync Library is enabled.

What happens when you try to import a CD to the Music app on your iMac? Are there any error messages?

When you say a mini iPod is syncing to the Apple Music service do you mean a HomePod mini? And what library did you initially match/sync with? How large was that library?

tt2

Press and hold down Option when launching Music and keep holding until prompted to choose or create a libary. Click choose and then browse to and open your library. This will normally be at ~/Music/Music/Music Library.musiclibrary. It seems Music may sometimes get connected to a cached version of the database that then doesn't update correctly. Close Music and this time hold down Option+Cmd as you relaunch it. There should be a message that it is opening in its safe mode, which may do some internal housekeeping. You can also right-click on the Music Library.musiclibrary package and select Show Package Contents. Check inside and use Shift+Cmd+. to show/hide hidden files. Check for any .tmp files. If these are present it indicates something is disturbing Music when it tries to save changes to the database. Delete them all. Disable any third party anti-virus software or add an exclusion for the Music folder.

tt2