Comment by Arathorn

MAS can be used as an OIDC IdP, and in future MAS will be embeddable in Synapse so you can use your homeserver as an IdP in the way you want, all in one package.

That said, MAS is deliberately not a very featureful IdP - it's focused on being the glue between Matrix and OIDC. If you want a more sophisticated IdP then you'll still want to run a dedicated one.