fix: join offloaded scheduler settlement

tests/scheduling/test_lifecycle.py

@@ -11,6 +11,7 @@ dedicated integration tests.
 from __future__ import annotations
 
 import asyncio
+import threading
 from datetime import UTC, datetime, timedelta
 from pathlib import Path
 from typing import Any, cast
@@ -238,6 +239,95 @@ async def test_scheduled_failure_records_failed_history(tmp_path: Path) -> None:
         await service.stop()
 
 
+async def test_settlement_does_not_block_the_event_loop(
+    tmp_path: Path, monkeypatch: Any
+) -> None:
+    """Synchronous settlement persistence must not stall other coroutines."""
+    intended = ts(2026, 9, 8, 12, 0)
+    service = _service(tmp_path, ScriptedRuntime("complete"))
+    settlement_started = threading.Event()
+    settlement_finished = threading.Event()
+    release = threading.Event()
+    original = Scheduler.record_stopped_execution
+
+    def _blocking_settle(self: Any, run_id: str, state: Any, now: datetime) -> None:
+        settlement_started.set()
+        release.wait(timeout=2)
+        original(self, run_id, state, now)
+        settlement_finished.set()
+
+    monkeypatch.setattr(Scheduler, "record_stopped_execution", _blocking_settle)
+    release_timer = threading.Timer(1.0, release.set)
+    release_timer.start()
+    try:
+        await service.start()
+        service.schedule_store.create_schedule(_sched_model("a", intended))
+        await service.poll_once(intended + timedelta(seconds=1))
+        await asyncio.sleep(0.05)
+        assert settlement_started.is_set()
+        assert not settlement_finished.is_set()
+        assert service.live_executions == 1
+        release.set()
+        await _wait_for(lambda: service.live_executions == 0)
+    finally:
+        release.set()
+        release_timer.cancel()
+        await service.stop()
+
+
+async def test_shutdown_joins_cancelled_settlement_before_releasing_ownership(
+    tmp_path: Path, monkeypatch: Any
+) -> None:
+    """Shutdown waits for an offloaded settlement after cancelling its task."""
+    intended = ts(2026, 9, 8, 12, 0)
+    service = _service(
+        tmp_path,
+        ScriptedRuntime("complete"),
+        SchedulerServiceConfig(
+            poll_interval_s=0.01,
+            drain_grace_s=0,
+            auto_tick=False,
+        ),
+    )
+    settlement_started = threading.Event()
+    release = threading.Event()
+    original = Scheduler.record_stopped_execution
+
+    def _blocking_settle(self: Any, run_id: str, state: Any, now: datetime) -> None:
+        settlement_started.set()
+        release.wait(timeout=2)
+        original(self, run_id, state, now)
+
+    monkeypatch.setattr(Scheduler, "record_stopped_execution", _blocking_settle)
+    release_timer = threading.Timer(1.0, release.set)
+    release_timer.start()
+    try:
+        await service.start()
+        service.schedule_store.create_schedule(_sched_model("a", intended))
+        await service.poll_once(intended + timedelta(seconds=1))
+        for _ in range(50):
+            if settlement_started.is_set():
+                break
+            await asyncio.sleep(0.01)
+        else:
+            pytest.fail("settlement did not start")
+
+        stop_task = asyncio.create_task(service.stop())
+        await asyncio.sleep(0.05)
+        assert not stop_task.done()
+        release.set()
+        report = await stop_task
+        assert report.settled == 1
+        assert report.cancelled == 0
+        assert service.run_store.get_run(
+            _only_run_id(service.run_store)
+        ).status.value == ("completed")
+    finally:
+        release.set()
+        release_timer.cancel()
+        await service.stop()
+
+
 async def test_scheduled_interrupt_stays_resumable(tmp_path: Path) -> None:
     intended = ts(2026, 9, 8, 12, 0)
     service = _service(tmp_path, ScriptedRuntime("interrupt"))