Concurrently collect room unread counts for push badges (#13765)

Most of the time this function is heavily cached, but when that isn't
the case fetching the counts room by room slows down push delivery on
users with many (thousands) of rooms.

Signed off by Nick @ Beeper.

changelog.d/13765.misc

@@ -0,0 +1 @@
+Concurrently fetch room push actions when calculating badge counts. Contributed by Nick @ Beeper (@fizzadar).

synapse/push/push_tools.py

@@ -17,6 +17,7 @@
 from synapse.push.presentable_names import calculate_room_name, name_from_member_event
 from synapse.storage.controllers import StorageControllers
 from synapse.storage.databases.main import DataStore
+from synapse.util.async_helpers import concurrently_execute
 
 
 async def get_badge_count(store: DataStore, user_id: str, group_by_room: bool) -> int:
@@ -25,13 +26,19 @@ async def get_badge_count(store: DataStore, user_id: str, group_by_room: bool) -
 
     badge = len(invites)
 
-    for room_id in joins:
-        notifs = await (
-            store.get_unread_event_push_actions_by_room_for_user(
+    room_notifs = []
+
+    async def get_room_unread_count(room_id: str) -> None:
+        room_notifs.append(
+            await store.get_unread_event_push_actions_by_room_for_user(
                 room_id,
                 user_id,
             )
         )
+
+    await concurrently_execute(get_room_unread_count, joins, 10)
+
+    for notifs in room_notifs:
         if notifs.notify_count == 0:
             continue