> One advantage of SAML over OIDC - they standardized IDP initiated login, so you can skip the "login using..." button when sending an already logged in user to a third party system.

OIDC supports this, though it is an optional part of the standard. This is the initiate_login_uri metadata on a relying party. https://openid.net/specs/openid-connect-core-1_0.html#ThirdP...