The problem is in Quick notes.
As you can try, if your last note is empty, the New note button is greyed and you cannot press it (even by cmd+N or menu).
Fill the new note and you can create another one.
Monterey introduced Quick notes. When the Quick note is empty, it behaves same and you cannot create New note.
Solution one: Fill your Quick note with some text
Solution two: Disable in Setting field Open last Quick note.
Always check if your last note contains something and is not blank.
(Apologies, my MacOS not in English language so the names of fields could slightly differ)
PavelStancik
Users receive reputation points by contributing quality content to the forums.
Posts include post and replies published on the forums.
Post authors can mark replies as Accepted to indicate successful solutions.
Apple Developer Forums admins can mark replies as Apple Recommended to indicate an approved solution