I lost access to literally nothing! SSO binds your email address as the primary account idenitifier in all known to me services.

Do you mean that you're setting up SAML/OpenID for every service you use?

Does not matter what IDP you use to “sign in with”.

I don't understand. The service provider needs to check the identity of the IdP, or IdP-B could impersonate user alice@foo belonging to IdP-A