Revert "Move start_doing_background_updates() to SynapseHomeServer.start_background_tasks() (#19036)"

This reverts commit d399d76.

Author: MadLittleMods

changelog.d/19036.misc

@@ -317,11 +317,6 @@ def start_listening(self) -> None:
                 # during parsing
                 logger.warning("Unrecognized listener type: %s", listener.type)
 
-    def start_background_tasks(self) -> None:
-        super().start_background_tasks()
-
-        self.get_datastores().main.db_pool.updates.start_doing_background_updates()
-
 
 def load_or_generate_config(argv_options: List[str]) -> HomeServerConfig:
     """
@@ -435,6 +430,11 @@ async def _start_when_reactor_running() -> None:
 
         await _base.start(hs, freeze)
 
+        # TODO: This should be moved to `SynapseHomeServer.start_background_tasks` (not
+        # `HomeServer.start_background_tasks`) (this way it matches the behavior of only
+        # running on `main`)
+        hs.get_datastores().main.db_pool.updates.start_doing_background_updates()
+
     # Register a callback to be invoked once the reactor is running
     register_start(hs, _start_when_reactor_running)