I was experiencing the same problem and what I found that worked for me was to first open Notes on my iPhone. Then in the dock on my Mac it would show 'Notes from iPhone' (not sure if this would work for the OP as Handoff may not have been introduced yet when the original post was made). Clicking that would open Notes in an 'unlocked' state with all Notes that were saved to iCloud as well as the ability to create new notes. However, if I was to click on the quick note in the bottom right of the screen (while Notes is closed) Notes would revert back to the 'locked' up state and I would have to go through this process again. YMMV Running MacOS Monterey (12.6) on a Mac M1 mini