Using the Apple Notes app and syncing it with a Gmail account will eventually clog your archive folder because every version of every note is stored as a separate email with the
Notes tag. Each time you update a note, the Notes app archives the old version and creates a new email.
Over time, this can become a real hindrance. For example, when searching for an old email, you may find that half of the results are old notes.
I looked high and low trying to find an easy way to delete old notes from Gmail without any success. However, thanks to some insights I gained, I experimentally arrived at the below search query to match all old note versions while excluding the latest version and all other emails.
from:YOUR_EMAIL_HERE@gmail.com -has:userlabels -in:sent -in:chat -in:draft -in:inbox
After searching for that query (be sure to replace the email address with your own), you can select all and then delete with one click!