fix: derive worker shutdown wait from timeout budget

Co-authored-by: Copilot App <[email protected]>

tests/test_app.py

@@ -28,6 +28,7 @@ class TestAppLifespan:
     def test_startup_initializes_runtime_dependencies(self, monkeypatch, tmp_path):
         """Startup initializes logging, schema, directories, and worker resources."""
         calls = []
+        worker_kwargs = {}
 
         monkeypatch.setattr("transcription.app.configure_logging", lambda _settings: calls.append("logging"))
         monkeypatch.setattr("transcription.app.register_pages", lambda _app: None)
@@ -53,6 +54,7 @@ class TestAppLifespan:
 
         @asynccontextmanager
         async def _worker_lifespan(**_kwargs):
+            worker_kwargs.update(_kwargs)
             calls.append("worker_start")
             yield object(), object(), object()
             calls.append("worker_stop")
@@ -78,6 +80,9 @@ class TestAppLifespan:
         assert "worker_start" in calls
         assert "worker_stop" in calls
         assert "dispose_db" in calls
+        assert worker_kwargs["shutdown_timeout_seconds"] == pytest.approx(
+            settings.worker_provider_timeout_seconds + settings.worker_shutdown_grace_seconds
+        )
         assert settings.upload_dir.exists()
         assert settings.prompt_dir.exists()