After MacOs update: "Google Authentication Fails", annoying pop up that won't go away, but Mail etc. works without problems

After I updated my OS recently, I'm getting popups asking me to to enter my Google password.

"Google Password Required

Enter your password for (google account name) in Internet Accounts

Close / Continue"

When I enter the password under Internet Accounts, I get "Authentication failed - Failed to authenticate with Google".

The password is correct (different error message when I enter a wrong one).

On Google itself, on the permissions page of my account, OsX is listed and all necessary permissions are given. Everything looks okay there.

I also can use my gmail without problems in Apple Mail.

The "Google Password Required" dialog pops up every 10 minutes and I can't find a way to deactivate it.

Is this problem on Apple's side or on Google's side? Any ideas what I can do to get rid of the pop up?