diff --git a/synapse/handlers/room_list.py b/synapse/handlers/room_list.py
index 1f37b57373..7e952f711a 100644
--- a/synapse/handlers/room_list.py
+++ b/synapse/handlers/room_list.py
@@ -27,14 +27,13 @@ from synapse.api.constants import (
     JoinRules,
     PublicRoomsFilterFields,
 )
-from synapse.types import Requester
 from synapse.api.errors import (
     Codes,
     HttpResponseException,
     RequestSendFailed,
     SynapseError,
 )
-from synapse.types import JsonDict, PublicRoom, ThirdPartyInstanceID
+from synapse.types import JsonDict, ThirdPartyInstanceID
 from synapse.util.caches.descriptors import _CacheContext, cached
 from synapse.util.caches.response_cache import ResponseCache
 
@@ -213,7 +212,7 @@ class RoomListHandler:
 
         response: JsonDict = {}
         num_results = len(results)
-        if limit is not None:
+        if limit is not None and probing_limit is not None:
             more_to_come = num_results >= probing_limit
 
             # Depending on direction we trim either the front or back.
diff --git a/synapse/module_api/__init__.py b/synapse/module_api/__init__.py
index 16bd966efe..e6d04b9dec 100644
--- a/synapse/module_api/__init__.py
+++ b/synapse/module_api/__init__.py
@@ -122,7 +122,6 @@ from synapse.types import (
     DomainSpecificString,
     JsonDict,
     JsonMapping,
-    PublicRoom,
     Requester,
     RoomAlias,
     StateMap,
diff --git a/synapse/module_api/callbacks/public_rooms_callbacks.py b/synapse/module_api/callbacks/public_rooms_callbacks.py
index 847becc89b..f12667d202 100644
--- a/synapse/module_api/callbacks/public_rooms_callbacks.py
+++ b/synapse/module_api/callbacks/public_rooms_callbacks.py
@@ -14,9 +14,9 @@
 
 import logging
 from typing import Awaitable, Callable, Iterable, List, Optional, Tuple
-from synapse.types import PublicRoom
 
-import attr
+
+from synapse.types import PublicRoom
 
 logger = logging.getLogger(__name__)
 
diff --git a/synapse/storage/databases/main/room.py b/synapse/storage/databases/main/room.py
index 67613ab90e..ec9691a5ce 100644
--- a/synapse/storage/databases/main/room.py
+++ b/synapse/storage/databases/main/room.py
@@ -16,7 +16,6 @@
 import logging
 from abc import abstractmethod
 from enum import Enum
-from synapse.api.constants import HistoryVisibility
 from typing import (
     TYPE_CHECKING,
     AbstractSet,
@@ -39,6 +38,7 @@ from synapse.api.constants import (
     Direction,
     EventContentFields,
     EventTypes,
+    HistoryVisibility,
     JoinRules,
     PublicRoomsFilterFields,
 )
@@ -543,7 +543,7 @@ class RoomWorkerStore(CacheInvalidationWorkerStore):
 
             # Filter out Nones – rather omit the field altogether
             for key in list(entry):
-                if entry[key] == None:
+                if entry[key] is None:
                     del entry[key]
 
             return entry
diff --git a/synapse/types/__init__.py b/synapse/types/__init__.py
index c593299a14..71be9b523f 100644
--- a/synapse/types/__init__.py
+++ b/synapse/types/__init__.py
@@ -27,6 +27,7 @@ from typing import (
     MutableMapping,
     NoReturn,
     Optional,
+    Required,
     Set,
     Tuple,
     Type,
@@ -953,15 +954,15 @@ class UserInfo:
     is_shadow_banned: bool
 
 
-class PublicRoom(TypedDict):
-    room_id: str
+class PublicRoom(TypedDict, total=False):
+    room_id: Required[str]
     name: Optional[str]
     topic: Optional[str]
-    num_joined_members: int
+    num_joined_members: Required[int]
     canonical_alias: Optional[str]
     avatar_url: Optional[str]
-    world_readable: bool
-    guest_can_join: bool
+    world_readable: Required[bool]
+    guest_can_join: Required[bool]
     join_rule: Optional[str]
     room_type: Optional[str]
 
diff --git a/tests/module_api/test_fetch_public_rooms.py b/tests/module_api/test_fetch_public_rooms.py
index 1486fbfab9..0d77cf6f74 100644
--- a/tests/module_api/test_fetch_public_rooms.py
+++ b/tests/module_api/test_fetch_public_rooms.py
@@ -11,22 +11,15 @@
 # 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 twisted.test.proto_helpers import MemoryReactor
-
 from http import HTTPStatus
 from typing import (
-    TYPE_CHECKING,
-    Callable,
-    Dict,
-    List,
-    Optional,
-    TypeVar,
-    Tuple,
-    cast,
     Iterable,
+    Optional,
+    Tuple,
 )
 
-from synapse.api.errors import SynapseError
+from twisted.test.proto_helpers import MemoryReactor
+
 from synapse.rest import admin, login, room
 from synapse.server import HomeServer
 from synapse.types import PublicRoom
@@ -119,4 +112,4 @@ class FetchPublicRoomsTestCase(HomeserverTestCase):
             "GET", self.url + "?limit=1&since=" + channel.json_body["next_batch"]
         )
         self.assertEqual(channel.code, HTTPStatus.OK, channel.result)
-        self.assertEquals(channel.json_body["chunk"][0]["num_joined_members"], 1)
\ No newline at end of file
+        self.assertEquals(channel.json_body["chunk"][0]["num_joined_members"], 1)