Always start the background process as it will clean up failed partia…

…l joins too

synapse/handlers/federation.py

@@ -546,9 +546,9 @@ async def do_invite_join(
             )
 
             if ret.partial_state:
-                # TODO(faster_joins): roll this back if we don't manage to start the
-                #   background resync (eg process_remote_join fails)
-                #   https://github.com/matrix-org/synapse/issues/12998
+                # Mark the room as having partial state.
+                # The background process is responsible for unmarking this flag,
+                # even if the join fails.
                 await self.store.store_partial_state_room(room_id, ret.servers_in_room)
 
             try:
@@ -574,17 +574,21 @@ async def do_invite_join(
                     room_id,
                 )
                 raise LimitExceededError(msg=e.msg, errcode=e.errcode, retry_after_ms=0)
-
-            if ret.partial_state:
-                # Kick off the process of asynchronously fetching the state for this
-                # room.
-                run_as_background_process(
-                    desc="sync_partial_state_room",
-                    func=self._sync_partial_state_room,
-                    initial_destination=origin,
-                    other_destinations=ret.servers_in_room,
-                    room_id=room_id,
-                )
+            finally:
+                # Always kick off the background process that asynchronously fetches
+                # state for the room.
+                # If the join failed, the background process is responsible for
+                # cleaning up — including unmarking the room as a partial state room.
+                if ret.partial_state:
+                    # Kick off the process of asynchronously fetching the state for this
+                    # room.
+                    run_as_background_process(
+                        desc="sync_partial_state_room",
+                        func=self._sync_partial_state_room,
+                        initial_destination=origin,
+                        other_destinations=ret.servers_in_room,
+                        room_id=room_id,
+                    )
 
             # We wait here until this instance has seen the events come down
             # replication (if we're using replication) as the below uses caches.