Udemy with email: Udemy gets your email, and will probably require a verification process to verify that you own it:

Udemy with Google Sign in: You click through in your browser, to authorize Udemy to obtain some details (usually just email + basic profile details), Udmey gets a "token" (effectively a random string) which they can send to google to retrieve these other details, and verify you still have an account and you (or google) haven't revoked access, which they can use now and in the future. They don't need to verify your email as they have a token that is "proof" already. To you it's a click through, to everyone else it's a bit more complex. If Udemy has a data leak, if they didn't store your email directly, it's possible that the token could be reset before someone is able to obtain it. But it's unlikely they aren't obtaining the email address as soon as you log in and storing it.