In addition to allowing Google to manage the authentication process, signing in with Google allows Google to track your visits. In some cases they get additional data about content you view.
In many cases the mere presence of that button allows Google to track that your device visited the Udemy sign in/sign up page, even if you don’t click it. Google uses this to create and update a profile of you they sell for advertising and other purposes, and exposes you to more risk if your Google account is breached. With a password manager I find using SSO to be about the same level of effort as using my manager’s autofill functionality
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