social_auth: Save authentication method information in the session.

The immediate application of this will be for SAML SP-initiated logout,
where information about which IdP was used for authenticating the
session needs to be accessed. Aside of that, this seems like generally
valuable session information to keep that other features may benefit
from in the future.

zproject/backends.py

@@ -1295,6 +1295,7 @@ class ExternalAuthDataDict(TypedDict, total=False):
     desktop_flow_otp: Optional[str]
     multiuse_object_key: str
     full_name_validated: bool
+    params_to_store_in_authenticated_session: Dict[str, str]
 
 
 class ExternalAuthResult:
@@ -1797,6 +1798,7 @@ def social_auth_finish(
         full_name_validated=full_name_validated,
         mobile_flow_otp=mobile_flow_otp,
         desktop_flow_otp=desktop_flow_otp,
+        params_to_store_in_authenticated_session=backend.get_params_to_store_in_authenticated_session(),
     )
     if user_profile is None:
         data_dict.update(dict(full_name=full_name, email=email_address))
@@ -1875,6 +1877,13 @@ class SocialAuthMixin(ZulipAuthMixin, ExternalAuthMethod, BaseAuth):
     def should_auto_signup(self) -> bool:
         return False
 
+    def get_params_to_store_in_authenticated_session(self) -> Dict[str, str]:
+        """
+        Specifies a dict of keys:values to be saved in the user's session
+        after successfully authenticating.
+        """
+        return {"authentication_method": self.name}
+
     @classmethod
     def dict_representation(cls, realm: Optional[Realm] = None) -> List[ExternalAuthMethodDictT]:
         return [
@@ -2701,6 +2710,11 @@ class SAMLAuthBackend(SocialAuthMixin, SAMLAuth):
         assert isinstance(auto_signup, bool)
         return auto_signup
 
+    def get_params_to_store_in_authenticated_session(self) -> Dict[str, str]:
+        idp_name = self.strategy.session_get("saml_idp_name")
+
+        return {"authentication_method": f"saml:{idp_name}"}
+
 
 def patch_saml_auth_require_messages_signed(auth: OneLogin_Saml2_Auth) -> None:
     """