Hello SnickZ., thank you for your reply!
I've tried many of the proposed solutions before, but it didn't help.
I started iTunes/Music again clicked into 4 albums in the iTunes Music Store and then the problems started. I took a look at the pop-up windows. The mouse and keyboard disconnect and reconnect all the time, apps in the menubar appear and disappear, the window freezes and then it's possible again to move the mouse for a short moment.
The Pop-Ups appear and disappear and appear again. The pop-up windows show the following messages. (They're in German, so I try to translate them):
Window 1: "CommCenter wants to use the keychain for "Login". Please enter your password for keychain."
Window 2: "callservicesd wants to use the keychain for "Login". Please enter your password for keychain."
Window 3: "iCloud Drive may not function correctly. Check the system configuration "iCloud". The communication with a helper app failed." There's a button: "Open Apple-ID settings." (Note from me: iCloud Drive is not activated).
Window 4: "sharingd wants to use the keychain for "Login". Please enter your password for keychain."
Then Window 1 reappears. I can't push anything on Window 3.
The comes Windows 5: "CallHistoryPluginHelper wants to use the keychain for "Login". Please enter your password for keychain."
Window 1 reappears plus Window 6: "Transparent network proxy for Apple system services wants to use the keychain for "Login". Please enter your password for keychain."
Then comes the message: "This Mac can't be connected to iMessage as there's a problem with your Apple-ID. Open the settings of your Apple-ID to solve the problem.
I finally unplugged my Mac Mini and restarted it. I only have the problems with Music and the iTunes store and they came with the update of MacOS 12.1
I read somewhere that Apple is working on a big change of the iTunes Store and Music and that the app will work much faster in the future. Maybe there's a problem with that?
Thank you for your help!