So you’ve done something, and the Notes app on the Mac won’t log in to Google anymore. It will sit and spin on a “logging in” forever.
Oh, and you’ve also just turned on two-factor auth in Google. Well, that’s the problem.
Google considers Notes to be a “less secure” app, and it won’t work with two-factor. What you need to do is create an app password, and then it will.
See also https://support.google.com/accounts/answer/185833
(Not saying two-factor auth is the problem. In fact, you should probably use it for everything.)