UIA: offer only available auth flows

During user-interactive auth, do not offer password auth to users with no
password, nor SSO auth to users with no SSO.

Fixes #7559.

synapse/storage/databases/main/registration.py

@@ -463,6 +463,23 @@ class RegistrationWorkerStore(CacheInvalidationWorkerStore):
             desc="get_user_by_external_id",
         )
 
+    async def get_external_ids_by_user(self, mxid: str) -> List[Tuple[str, str]]:
+        """Look up external ids for the given user
+
+        Args:
+            mxid: the MXID to be looked up
+
+        Returns:
+            Tuples of (auth_provider, external_id)
+        """
+        res = await self.db_pool.simple_select_list(
+            table="user_external_ids",
+            keyvalues={"user_id": mxid},
+            retcols=("auth_provider", "external_id"),
+            desc="get_external_ids_by_user",
+        )
+        return [(r["auth_provider"], r["external_id"]) for r in res]
+
     async def count_all_users(self):
         """Counts all users registered on the homeserver."""
 
@@ -963,6 +980,14 @@ class RegistrationBackgroundUpdateStore(RegistrationWorkerStore):
             "users_set_deactivated_flag", self._background_update_set_deactivated_flag
         )
 
+        self.db_pool.updates.register_background_index_update(
+            "user_external_ids_user_id_idx",
+            index_name="user_external_ids_user_id_idx",
+            table="user_external_ids",
+            columns=["user_id"],
+            unique=False,
+        )
+
     async def _background_update_set_deactivated_flag(self, progress, batch_size):
         """Retrieves a list of all deactivated users and sets the 'deactivated' flag to 1
         for each of them.