test(alerts): wait for the alert's tasks and the run, not every task (#5063)

CI 8343: the wait-for-all-tasks loop also waited on the executor's
5-minute run-output cleanup task (_schedule_cleanup) and hit its 120s
deadline. Wait on alerts._background, then poll the run to a final status.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/integration/test_alert_ansible_action.py

@@ -83,13 +83,23 @@ def test_firing_triggers_ansible_action(app, tmp_path):
             async with s.begin():
                 await record_metric(s, "host_agent", "srv1", "cpu_pct", 95.0)
 
-        # Let the dispatch, the action and the run it starts finish. The run's
-        # task is created by the action's task, so wait until none are left.
+        # Let the notification and the action finish, then the run the action
+        # started. Not "every task": a finished run leaves a cleanup task that
+        # sleeps for minutes (executor._schedule_cleanup).
+        from steward.core import alerts
         loop = asyncio.get_running_loop()
         deadline = loop.time() + 120
-        while pending := [t for t in asyncio.all_tasks() if t is not asyncio.current_task()]:
-            assert loop.time() < deadline, f"tasks still running: {pending}"
-            await asyncio.wait(pending, timeout=deadline - loop.time())
+        while alerts._background:
+            assert loop.time() < deadline, "the alert's tasks did not finish"
+            await asyncio.wait(set(alerts._background), timeout=deadline - loop.time())
+        while True:
+            async with app.db_sessionmaker() as s:
+                status = (await s.execute(
+                    select(AnsibleRun.status).where(AnsibleRun.source_name == "t"))).scalar()
+            if status not in (None, AnsibleRunStatus.queued, AnsibleRunStatus.running):
+                break
+            assert loop.time() < deadline, f"the run is still {status}"
+            await asyncio.sleep(0.5)
 
         async with app.db_sessionmaker() as s:
             run = (await s.execute(