Hello Talik3,
Welcome to Apple Support Communities!
If we understand your post correctly, there is no back button in Apple Music after installing Monterey on your Mac. Reviewing the article Listen to Apple Music on the web and in apps was a good starting point. We'd like to help!
We recommend starting in safe mode. Sometimes just starting in this mode and then restarting can resolve issues like this: How to use safe mode on your Mac
You can also create another user on your Mac and test to see if you experience the same issue.
Set up users, guests, and groups on Mac
Let us know if you have any questions.
Thank you for using Apple Support Communities.
Take care!