Make pushers use the event_push_actions table instead of listening on an event stream & running the rules again. Sytest passes, but remaining to do:

* Make badges work again
 * Remove old, unused code

synapse/handlers/_base.py

@@ -21,7 +21,7 @@ from synapse.api.constants import Membership, EventTypes
 from synapse.types import UserID, RoomAlias, Requester
 from synapse.push.action_generator import ActionGenerator
 
-from synapse.util.logcontext import PreserveLoggingContext
+from synapse.util.logcontext import PreserveLoggingContext, preserve_fn
 
 import logging
 
@@ -377,6 +377,12 @@ class BaseHandler(object):
             event, context=context
         )
 
+        # this intentionally does not yield: we don't care about the result
+        # and don't need to wait for it.
+        preserve_fn(self.hs.get_pusherpool().on_new_notifications)(
+            event_stream_id, max_stream_id
+        )
+
         destinations = set()
         for k, s in context.current_state.items():
             try: