Add index to sliding_sync_membership_snapshots(membership_event_id)

To address a performance problem due to the foreign key on the same
column.

synapse/storage/databases/main/sliding_sync.py

@@ -1,7 +1,7 @@
 #
 # This file is licensed under the Affero General Public License (AGPL) version 3.
 #
-# Copyright (C) 2023 New Vector, Ltd
+# Copyright (C) 2023, 2025 New Vector, Ltd
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU Affero General Public License as
@@ -61,6 +61,13 @@ def __init__(
             columns=("required_state_id",),
         )
 
+        self.db_pool.updates.register_background_index_update(
+            update_name="sliding_sync_membership_snapshots_membership_event_id_idx",
+            index_name="sliding_sync_membership_snapshots_membership_event_id_idx",
+            table="sliding_sync_membership_snapshots",
+            columns=("membership_event_id",),
+        )
+
     async def get_latest_bump_stamp_for_room(
         self,
         room_id: str,

synapse/storage/schema/main/delta/88/07_sliding_sync_membership_snapshot_index.sql

@@ -0,0 +1,15 @@
+--
+-- This file is licensed under the Affero General Public License (AGPL) version 3.
+--
+-- Copyright (C) 2025 New Vector, Ltd
+--
+-- This program is free software: you can redistribute it and/or modify
+-- it under the terms of the GNU Affero General Public License as
+-- published by the Free Software Foundation, either version 3 of the
+-- License, or (at your option) any later version.
+--
+-- See the GNU Affero General Public License for more details:
+-- <https://www.gnu.org/licenses/agpl-3.0.html>.
+
+INSERT INTO background_updates (ordering, update_name, progress_json) VALUES
+    (8807, 'sliding_sync_membership_snapshots_membership_event_id_idx', '{}');