Rebuild the user directory and stats tables. (#14643)

Due to the various fixes to the StreamChangeCache it is not
safe to trust the information in the user directory or room/user
stats tables. Rebuild them as background jobs.

In particular see da77720 (#14639),
and 6a8310f (#14435).

Maybe also be related to fac8a38
(#14592).

changelog.d/14643.bugfix

@@ -0,0 +1 @@
+Fix a long-standing bug where the user directory and room/user stats might be out of sync.

synapse/storage/schema/main/delta/73/22_rebuild_user_dir_stats.sql

@@ -0,0 +1,29 @@
+/* Copyright 2022 The Matrix.org Foundation C.I.C
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+INSERT INTO background_updates (ordering, update_name, progress_json, depends_on) VALUES
+  -- Set up user directory staging tables.
+  (7322, 'populate_user_directory_createtables', '{}', NULL),
+  -- Run through each room and update the user directory according to who is in it.
+  (7322, 'populate_user_directory_process_rooms', '{}', 'populate_user_directory_createtables'),
+  -- Insert all users into the user directory, if search_all_users is on.
+  (7322, 'populate_user_directory_process_users', '{}', 'populate_user_directory_process_rooms'),
+  -- Clean up user directory staging tables.
+  (7322, 'populate_user_directory_cleanup', '{}', 'populate_user_directory_process_users'),
+  -- Rebuild the room_stats_current and room_stats_state tables.
+  (7322, 'populate_stats_process_rooms', '{}', NULL),
+  -- Update the user_stats_current table.
+  (7322, 'populate_stats_process_users', '{}', NULL)
+ON CONFLICT (update_name) DO NOTHING;