Mozilla Persona was deaigned so "the identity provider does not know which website the user is identifying on." But it did nto catch on.
As a user, it seemed like "so i need to login to Google on Mozilla.org... it's just a wrapper for my Gmail and/or Mozilla account?"
You can rent it from AWS, of course. It's called Cognito.
https://aws.amazon.com/cognito/
You can also offload that responsibility for user data/credentials to Google/Facebook et al as you see many places with "Login with Facebook", making your users pay in privacy-invasion instead of bearing the burden of properly securing your user's PII yourself...