What is the point of signing up with oauth2 if it is a paid subscription site?

I understand what oauth2 is and I programmed it in one of our projects. It was about transferring user data from an oauth2 provider (Facebook, Google, etc.) to our application (for example, the user's 10 most recent e-mails). It was very convenient for this purpose.

Now I'm trying to think about why a web designer wants to include oauth2 as a means of logging into their site. I can see that it is useful for a free website. If the user does not want to create their own account for the website, they can simply use an existing account with an oauth2 provider (Facebook, Google, etc.). They simply log in to the oauth2 provider, are redirected back to the site with the access token, and use that access token to navigate the site. The website essentially "shares" the access token between itself and the oauth2 provider (as I said: as long as you are logged in to Facebook, you are also logged in to our website).

But what about a site that requires a paid subscription to sign up? In this case, you do not want the user to log in using another oauth2 provider. In this way, the user can bypass signing up for a subscription. I think you could Send a request to the oauth2 provider (once you have the access token) to get the user's information. Map this information in the database of the website to an entry indicating that the user has signed up for a paid subscription. Otherwise, you deny access. If access is denied, redirect the user to sign up for a subscription. But is oauth2 login ever used that way?

How does it work if oauth2 login is used by websites whose membership requires a paid subscription? How, for example, does Facebook know that you've signed up for a subscription on the website of a client app, and therefore grants you the access token? Or does it work the way I described it?