Fix sending presence over federation when using workers

When using a federation sender we'd send out all local presence updates over
federation even when they shouldn't be.

Fixes #10153.

synapse/handlers/presence.py

@@ -495,9 +495,6 @@ async def notify_from_replication(
             users=users_to_states.keys(),
         )
 
-        # If this is a federation sender, notify about presence updates.
-        await self.maybe_send_presence_to_interested_destinations(states)
-
     async def process_replication_rows(
         self, stream_name: str, instance_name: str, token: int, rows: list
     ):
@@ -519,11 +516,27 @@ async def process_replication_rows(
             for row in rows
         ]
 
-        for state in states:
-            self.user_to_current_state[state.user_id] = state
+        # The list of states to notify sync streams and remote servers about.
+        # This is calculated by comparing the old and new states for each user
+        # using `should_notify(..)`.
+        #
+        # Note that this is necessary as the presence writer will periodically
+        # flush presence state changes that should not be notified about to the
+        # DB, and so will be sent over the replication stream.
+        state_to_notify = []
+
+        for new_state in states:
+            old_state = self.user_to_current_state.get(new_state.user_id)
+            self.user_to_current_state[new_state.user_id] = new_state
+
+            if not old_state or should_notify(old_state, new_state):
+                state_to_notify.append(new_state)
 
         stream_id = token
-        await self.notify_from_replication(states, stream_id)
+        await self.notify_from_replication(state_to_notify, stream_id)
+
+        # If this is a federation sender, notify about presence updates.
+        await self.maybe_send_presence_to_interested_destinations(state_to_notify)
 
     def get_currently_syncing_users_for_replication(self) -> Iterable[str]:
         return [