Apple =Notes on Mac New Note greyed out - can't make new notes solution
This has been happenning every now again on Monterey
Easy Fix
Open Mac OS settings apple top left corner - Preferences...
Open Icloud profile (not family sharing) (top line)
in the right hand block see notes ticked to sync in Icloud
Untick it (untick blue x in Notes)- wait a few seconds
Tick it to show a blue tick again.
Will reset to allow new messages.
Seems to be a bug i find in Notes in Monterey
May need resetting like this again now and Again.