Remove delay when rotating event push actions (#13211)

We want to be as up to date as possible, and sleeping doesn't help here
and can mean we fall behind.

changelog.d/13211.misc

@@ -0,0 +1 @@
+More aggressively rotate push actions.

synapse/storage/databases/main/event_push_actions.py

@@ -143,7 +143,6 @@ class EventPushActionsWorkerStore(ReceiptsWorkerStore, StreamWorkerStore, SQLBas
             self._find_stream_orderings_for_times, 10 * 60 * 1000
         )
 
-        self._rotate_delay = 3
         self._rotate_count = 10000
         self._doing_notif_rotation = False
         if hs.config.worker.run_background_tasks:
@@ -847,7 +846,6 @@ class EventPushActionsWorkerStore(ReceiptsWorkerStore, StreamWorkerStore, SQLBas
                 )
                 if caught_up:
                     break
-                await self.hs.get_clock().sleep(self._rotate_delay)
 
             # Finally we clear out old event push actions.
             await self._remove_old_push_actions_that_have_rotated()
@@ -1114,7 +1112,7 @@ class EventPushActionsWorkerStore(ReceiptsWorkerStore, StreamWorkerStore, SQLBas
         ) -> bool:
             # We don't want to clear out too much at a time, so we bound our
             # deletes.
-            batch_size = 10000
+            batch_size = self._rotate_count
 
             txn.execute(
                 """