it's a tale of two protocols, Office365 supports quick configuration of applications that support the OpenIDConnect protocol, it's likely you signed into this site with an OpenID provided by some trusted identity provider:
(you should be able to sign in here with an OpenID provided by your O365)
SAML 2.0 is the more complete implementation of a Web SSO but uses SOAP/XML - whereas OpenIDConnect users RESTful/JSON and service providers/Resource Servers (Apps) can be dynamically registered, but much other functionality you will look for will be 'out of scope'
Thee AzureAD SAML identity provider is not a full implementation of the protocol and it does not support the eduperson schema, neither will it download metadata from a URL (say from a federation).
Microsoft are members of the OpenID foundation along with many other commercial vested interests such as Google, Facebook, Paypal or anyone else with an 'all of your user are belong to us' mentality, so naturally they cripple Azure AD from doing anything useful other that supporting basic functionality - want to grant a group of users access to some app from the Portal? - that's Azure AD premium! - The portal btw is just a thrown together list of applications that support OpenID logins - SF may as well be listed there, it doesn't mean anything, it's just a lot of whizz bangerery, the have also listed apps that support the SAML protocol and these will require some configuration of Azure AD and some configuration of the app in question - so it's actually pointless even listing these ones (in the flashy portal) other than to let you know 'this app supports SAML'.
Azure AD will also support an authentication proxy, where an app doesn't support an SSO protocol it can be configured for a one time authentication and there after remember the credentials, so it does expose these brutal hacks too. What's funny about the AzureAD and Office365 cool aide is that it all begins with a DirSync - the very evil that these protocols where invented to address - Here! have all my users??? - so in that respect AzureAD is all fur coat and no knickers.
You can run all of this on Domain, a full implementation of SAML with Shibboleth or a bundled SSO protocol stack with SAML and OpenIDConnect with something like gluu https://www.gluu.org/gluu-server/overview/ it's not crippled, is free and you don't have to give all of your users to some third party with an agenda.
I'm not recommending any of the above - I'm just letting you know that you don't need AzureAD and the more involved you get in identity federation the more of a barrier it will become without the 'premium features' of 2 protocols that community volunteers worked their asses off to deliver.