Clean up an indirect reference to the homeserver datastore

changelog.d/11914.misc

@@ -0,0 +1 @@
+Various refactors to the typing notifications code.

synapse/handlers/typing.py

@@ -446,7 +446,7 @@ def process_replication_rows(
 
 class TypingNotificationEventSource(EventSource[int, JsonDict]):
     def __init__(self, hs: "HomeServer"):
-        self.hs = hs
+        self._main_store = hs.get_datastore()
         self.clock = hs.get_clock()
         # We can't call get_typing_handler here because there's a cycle:
         #
@@ -487,7 +487,7 @@ async def get_new_events_as(
                     continue
 
                 if not await service.matches_user_in_member_list(
-                    room_id, handler.store
+                    room_id, self._main_store
                 ):
                     continue