Fix the rest of the MultiSSOTestCase tests

tests/rest/client/test_login.py

@@ -745,6 +745,30 @@ def test_multi_sso_redirect_to_cas(self) -> None:
             + "&idp=cas",
             shorthand=False,
         )
+        self.assertEqual(channel.code, 302, channel.result)
+        location_headers = channel.headers.getRawHeaders("Location")
+        assert location_headers
+        sso_login_redirect_uri = location_headers[0]
+
+        # it should redirect us to the standard login SSO redirect flow
+        self.assertEqual(
+            sso_login_redirect_uri,
+            self.login_sso_redirect_url_builder.build_login_sso_redirect_uri(
+                idp_id="cas", client_redirect_url=TEST_CLIENT_REDIRECT_URL
+            ),
+        )
+
+        # follow the redirect
+        #
+        # We have to make this relative to be compatible with `make_request(...)`
+        relative_sso_login_redirect_uri = get_relative_uri_from_absolute_uri(
+            sso_login_redirect_uri
+        )
+        channel = self.make_request(
+            "GET",
+            relative_sso_login_redirect_uri,
+        )
+
         self.assertEqual(channel.code, 302, channel.result)
         location_headers = channel.headers.getRawHeaders("Location")
         assert location_headers
@@ -770,6 +794,30 @@ def test_multi_sso_redirect_to_saml(self) -> None:
             + urllib.parse.quote_plus(TEST_CLIENT_REDIRECT_URL)
             + "&idp=saml",
         )
+        self.assertEqual(channel.code, 302, channel.result)
+        location_headers = channel.headers.getRawHeaders("Location")
+        assert location_headers
+        sso_login_redirect_uri = location_headers[0]
+
+        # it should redirect us to the standard login SSO redirect flow
+        self.assertEqual(
+            sso_login_redirect_uri,
+            self.login_sso_redirect_url_builder.build_login_sso_redirect_uri(
+                idp_id="saml", client_redirect_url=TEST_CLIENT_REDIRECT_URL
+            ),
+        )
+
+        # follow the redirect
+        #
+        # We have to make this relative to be compatible with `make_request(...)`
+        relative_sso_login_redirect_uri = get_relative_uri_from_absolute_uri(
+            sso_login_redirect_uri
+        )
+        channel = self.make_request(
+            "GET",
+            relative_sso_login_redirect_uri,
+        )
+
         self.assertEqual(channel.code, 302, channel.result)
         location_headers = channel.headers.getRawHeaders("Location")
         assert location_headers
@@ -881,12 +929,36 @@ def test_login_via_oidc(self) -> None:
         self.assertEqual(chan.json_body["user_id"], "@user1:test")
 
     def test_multi_sso_redirect_to_unknown(self) -> None:
-        """An unknown IdP should cause a 400"""
+        """An unknown IdP should cause a 404"""
         channel = self.make_request(
             "GET",
             "/_synapse/client/pick_idp?redirectUrl=http://x&idp=xyz",
         )
-        self.assertEqual(channel.code, 400, channel.result)
+        self.assertEqual(channel.code, 302, channel.result)
+        location_headers = channel.headers.getRawHeaders("Location")
+        assert location_headers
+        sso_login_redirect_uri = location_headers[0]
+
+        # it should redirect us to the standard login SSO redirect flow
+        self.assertEqual(
+            sso_login_redirect_uri,
+            self.login_sso_redirect_url_builder.build_login_sso_redirect_uri(
+                idp_id="xyz", client_redirect_url="http://x"
+            ),
+        )
+
+        # follow the redirect
+        #
+        # We have to make this relative to be compatible with `make_request(...)`
+        relative_sso_login_redirect_uri = get_relative_uri_from_absolute_uri(
+            sso_login_redirect_uri
+        )
+        channel = self.make_request(
+            "GET",
+            relative_sso_login_redirect_uri,
+        )
+
+        self.assertEqual(channel.code, 404, channel.result)
 
     def test_client_idp_redirect_to_unknown(self) -> None:
         """If the client tries to pick an unknown IdP, return a 404"""