Note that AS interest via room ID or alias isn't respected

Typing and read receipt events (those that are associated with a room)
should be sent to an AS that has registered interest in that room,
according to MSC2409:

231084da13/proposals/2409-appservice-edus.md (expectations-of-when-an-edu-should-be-pushed-to-an-appservice)

synapse/handlers/receipts.py

@@ -267,6 +267,10 @@ class ReceiptEventSource(EventSource[int, JsonDict]):
         )
 
         # Then filter down to rooms that the AS can read
+        # TODO: This doesn't seem to honour an appservice's registration of room or
+        #   namespace aliases. For instance, if an appservice registered a room namespace
+        #   that matched this room, but it didn't have any members in the room, then that
+        #   appservice wouldn't receive the read receipt.
         events = []
         for room_id, event in rooms_to_events.items():
             if not await service.matches_user_in_member_list(room_id, self.store):

synapse/handlers/typing.py

@@ -481,6 +481,11 @@ class TypingNotificationEventSource(EventSource[int, JsonDict]):
             for room_id in handler._room_serials.keys():
                 if handler._room_serials[room_id] <= from_key:
                     continue
+
+                # TODO: This doesn't seem to honour an appservice's registration of room or
+                #   namespace aliases. For instance, if an appservice registered a room namespace
+                #   that matched this room, but it didn't have any members in the room, then that
+                #   appservice wouldn't receive the typing event.
                 if not await service.matches_user_in_member_list(
                     room_id, handler.store
                 ):