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

(more sane standard location for this sort of thing)

The one difference here is that previously, `start_doing_background_updates
()` only ran on the main Synapse instance. But since it now lives in
`start_background_tasks()`, it will run on the worker that supposed to
`run_background_tasks`. Doesn't seem like a problem though.

Author: MadLittleMods

changelog.d/19036.misc

@@ -0,0 +1 @@
+Move `start_doing_background_updates()` to `SynapseHomeServer.start_background_tasks()`.

synapse/app/homeserver.py

@@ -317,6 +317,11 @@ 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:
     """
@@ -430,11 +435,6 @@ 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)