Fix bug with new task scheduler using lots of CPU. (#16278)

Using the new `TaskScheduler` meant that we'ed create lots of new
metrics (due to adding task ID to the desc of background process),
resulting in requests for metrics taking an increasing amount of CPU.

changelog.d/16278.misc

@@ -0,0 +1 @@
+Fix using the new task scheduler causing lots of CPU to be used.

synapse/util/task_scheduler.py

@@ -19,6 +19,7 @@ from prometheus_client import Gauge
 
 from twisted.python.failure import Failure
 
+from synapse.logging.context import nested_logging_context
 from synapse.metrics.background_process_metrics import run_as_background_process
 from synapse.types import JsonMapping, ScheduledTask, TaskStatus
 from synapse.util.stringutils import random_string
@@ -316,6 +317,7 @@ class TaskScheduler:
         function = self._actions[task.action]
 
         async def wrapper() -> None:
+            with nested_logging_context(task.id):
                 try:
                     (status, result, error) = await function(task)
                 except Exception:
@@ -353,5 +355,4 @@ class TaskScheduler:
 
         self._running_tasks.add(task.id)
         await self.update_task(task.id, status=TaskStatus.ACTIVE)
-        description = f"{task.id}-{task.action}"
-        run_as_background_process(description, wrapper)
+        run_as_background_process(task.action, wrapper)