Google ask for authentication via web browser, when using APPLE MAIL, but link brings me to Microsoft authentication

I have a google email account - and I access it through Apple Mail. However, Google asks in Mac OSX12.4 that I authenticate via my web browser. When I follow the link in the pop-up presented, I get a Microsoft authentication page which, naturally, does not recognise my Gmail account.

Please help - how can this be happening? I don't know how to get help on it.