Fix "Re-starting finished log context" spam when creating events (#14947)

`run_in_background` calls re-use the current logging context. When they
are not awaited, they can complete after the current logging context has
been marked as finished, which leads to log spam. Use
`run_as_background_process` instead.

Fixes one of the instances of #13090.

Signed-off-by: Sean Quah <seanq@matrix.org>

changelog.d/14947.bugfix

@@ -0,0 +1 @@
+Fix a long-standing bug where sending messages on servers with presence enabled would spam "Re-starting finished log context" log lines.

synapse/handlers/message.py

@@ -1939,7 +1939,9 @@ class EventCreationHandler:
             if event.type == EventTypes.Message:
                 # We don't want to block sending messages on any presence code. This
                 # matters as sometimes presence code can take a while.
-                run_in_background(self._bump_active_time, requester.user)
+                run_as_background_process(
+                    "bump_presence_active_time", self._bump_active_time, requester.user
+                )
 
         async def _notify() -> None:
             try: