Fix `RetryDestinationLimiter` re-starting finished log contexts (#12803)

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

changelog.d/12803.bugfix

+Fix a long-standing bug where finished log contexts would be re-started when failing to contact remote homeservers.

synapse/util/retryutils.py

@@ -16,8 +16,8 @@ import random
 from types import TracebackType
 from typing import TYPE_CHECKING, Any, Optional, Type
 
-import synapse.logging.context
 from synapse.api.errors import CodeMessageException
+from synapse.metrics.background_process_metrics import run_as_background_process
 from synapse.storage import DataStore
 from synapse.util import Clock
 
@@ -265,4 +265,4 @@ class RetryDestinationLimiter:
                 logger.exception("Failed to store destination_retry_timings")
 
         # we deliberately do this in the background.
-        synapse.logging.context.run_in_background(store_retry_timings)
+        run_as_background_process("store_retry_timings", store_retry_timings)