(Sorry if this is too basic, I'm not a web dev)
When a third-party web site offers you to "sign in with Google", what risks are you taking: Are you just giving it (the third party) your name and gmail address, or are you giving it anything else just by signing in?
As @Tetsujin mentions, you share personal data with Google they would not otherwise have. You also share with the other account information from Google that they would not otherwise have.
Another risk is that you have inserted a dependency of requiring that particular Google account to access and use your other account. You lose access to your other account if you lose access to your Google account, or the other account stops supporting Google sign-in, or if Google drops that other service due to legal / political / other issues.
If your Google account gets hacked or breached, you put the other account at risk.
If you use sign in with Google on a lot of other accounts, you have a pretty large single point of failure.
When you click on that button, it will redirect to Google's sign in page, and once you sign in, Google should show you what information of your Google account is shared. Some websites might also allow you to enable/disable the sharing of certain info.
Most social media apps should just need name, email, avatar. Other apps might need more depending on what they do/want.
I would consider the main 'risk' being that by using the service, you are contributing your personal 'interest list' to an organisation whose entire raison d'être is to sell targeted advertising to 3rd parties.
I would see that as sufficient reason to never use this type of service.
