You have reported at least 3 different problems. Let me try to address some of them.
1. Menus in MC31 with Sonoma are a known problem. JRiver staff are working on fixing them.
2. Sound buffering: Let's address that a bit later to make things more simple to start.
3. Missing albums and "importing". MC for Mac isn't as automatic in finding your old installation as the Windows version. What your really want to do, when you install a new MC for Mac, is to RESTORE A LIBRARY BACKUP from your current MC version. MC makes automatic library backups. They are normally in <your user>/Documents/JRiver/<jriver version> backups/
Take a look and see if you can find your backups from MC28. Then, in MC31: File > Library > Restore Library . Then select the latest backup from MC28.
That should show you everything that you saw in MC28, exactly as you saw it. You will need to restart MC31 for it to fully take effect. This is because it restores both the Library data and the settings.
I'm hoping that when it restores your settings, you will also have your audio working correctly at that point. If not, someone can try to help you get the audio working at that point.
Best of luck,
Brian.