Update Mutual Rooms (MSC2666) implementation (#15621)

To track changes in MSC2666:

- The change from `/mutual_rooms/{user_id}` to `/mutual_rooms?user_id={user_id}`.
- The addition of `next_batch_token` (and logic).
- Unstable flag now being `uk.half-shot.msc2666.query_mutual_rooms`.
- The error code when your own user is requested.

tests/rest/client/test_mutual_rooms.py

@@ -11,6 +11,8 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+from urllib.parse import quote
+
 from twisted.test.proto_helpers import MemoryReactor
 
 import synapse.rest.admin
@@ -44,8 +46,8 @@ class UserMutualRoomsTest(unittest.HomeserverTestCase):
     def _get_mutual_rooms(self, token: str, other_user: str) -> FakeChannel:
         return self.make_request(
             "GET",
-            "/_matrix/client/unstable/uk.half-shot.msc2666/user/mutual_rooms/%s"
-            % other_user,
+            "/_matrix/client/unstable/uk.half-shot.msc2666/user/mutual_rooms"
+            f"?user_id={quote(other_user)}",
             access_token=token,
         )