Overwritten Mac note
There’s nothing to recover.


Notes is autosaved the moment you make a change, so it saved your deletion
You didn’t delete the file, you changed it’s contents so recovery software can’t help.  No software can distinguish the difference between “Oops” and “I meant to do that”
Cloud storage isn’t back up, it’s file synchronization for availability everywhere.  That saved file was synced to all of your devices when it changed.
Time machine would be the best way to protect your data. This needs to be configured and used.


Now, if you do use iCloud, but it just wasn't “on” during this period, it may be your saving grace.  Using a different computer, log into your iCloud account (iCloud drive) via a web browser and download a copy of your notes.  Make a backup of this file!  

Now, if you log back into your computer, you can copy the notes back and have it sync.  Then turn on a Time Machine.