This already somewhat exists in the form of LTIs[0] and the Common Cartridge format[1], which are standards for application interoperability (i.e, how an app exchanges data with an LMS) and data exchange (export course content from one LMS and bring it into another), respectively. Social identity isn't really used, instead most institutions use Shibboleth/Gsuite/Azure AD as a SAML Auth gateway that authenticates users to services. All of these standards are supported by Blackboard, Canvas, Moodle and pretty much every other LMS that wants to get traction now (since all your other software expects it).

0: https://www.imsglobal.org/activity/learning-tools-interopera...

1: https://www.imsglobal.org/activity/common-cartridge