Working fine for me with five Google accounts. I'd just remove your Google account from System Preferences > Internet Accounts. Then add it back. That usually clears up issues.
If it still doesn't work. Check your Google security settings. See if there are any alerts. As it may have blocked your computer for some reason. Unless you manually configured the account. It shouldn't be a Less Secure App issue. Since Apple follows Apple's current secure login requirements.
myaccount.google.com