Finally figured it out... After following all of the Apple troubleshooting tips, with Connection Doctor, updating password in server list, restarting, and (almost) deleting/recreating the Gmail account, it turns out that Gmail login/password used by Mail is (ignored) in Mail. You must go elsewhere to confirm your Gmail password.
Open System Preferences. Select Internet Accounts. Select the Gmail account (I know, you're not in Mail, but MacOS ignores the fact that it is just a Mail account)... It should prompt for the password, then Mail works. While they may have a reason to separate Gmail from, well, Gmail, at least make the "it's in System Preferences->Internet Accounts" more obvious, instead of all the historical troubleshooting that doesn't work (except deleting and re-adding your account)...