Authentication failed to add google in internet accounts

If Mail on your Mac keeps asking for your password

• Your email provider needs you to update or reset your password for security reasons. For example, if you're using Google’s two-step verification, your Gmail account in Mail requires the appropriate app-specific password.
• Your email provider deactivated or suspended your account. Contact your email provider for help.

You need to create an app specific password.

https://support.google.com/accounts/answer/185833?hl=en

Try:

https://discussions.apple.com/thread/253304132

Can't add google account to Monterey