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

It’s impossible to do without signing the with the valid cert. I think destroying the anonymity is the point

No you’re right. The ARF just ignored that constraint and intentionally built in a back door here. From the linked article:

However, the current ARF stipulates that law enforcement authorities can retroactively trace pseudonyms back to their legal identity. The provisions therefore „strongly contradicts the legal requirements,“ epicenter.works writes.

If they are checking data brokers or aggregators it’s not really a background check. Carefully read any consent you give for a potential employer to perform a background check. Look for the records they are accessing and make a determination based on that language.

It is possible that some vendor is the space incorporates data brokers into their service, and that’s hard to tell. But they still should ask for your consent, I believe.