Connected accounts and social login
Updated
Today, the only way to sign in to My Hangar is an email and a password. There are no connected accounts to manage, and no Google, Apple or other social login.
If you are looking for a button that isn't there
You did not miss a setting. Sign in with the address you registered and its password. If you do not remember the password, reset it. If you never finished signing up, confirm your email or start again.
Other services
The share sheet on your phone can send a challenge link to any app, but that connects nothing: My Hangar gets no access to that app. Paying is done on Stripe's pages and Stripe's terms apply there, but that is not a login either.