Could you post a screenshot that shows that a) automatic backups are on and b) there is no "Next backup:"? That definitely sounds like unexpected behavior.
First thing I'd try is a test user. You would go to System Preferences > Users & Groups and create a new user. The name and password don't matter, just be sure it's an administrator rather than standard account. Then, log out ( Apple Menu > Log Out [name]) and into the new user. You don't need to sign in with the Apple id when it asks you to. You'll then want to attempt creating an automatic backup. If that works, the issue is something related to your user account data. It can be hard to narrow down from there. Otherwise, the issue is with system data, and you may want to consider reinstalling macOS as a troubleshooting step.
The user guide article doesn't have information specific to automatic backup troubleshooting. It does mention being up to date. I know you said monterey, is it running the latest version (12.4)?
Time Machine troubleshooting on Mac - Apple Support