Run the missed sweep in the API and publish quest-missed on SSE

WHY: The nightly missed-quest sweep only existed on the Home
Assistant plane (the rollover listener fired hass.bus), so the API
service - now the writer of record with its own settings store and
SSE stream - had no way to announce missed quests, and an admin
could not trigger a catch-up run after downtime.

- Extract the sweep policy (watermark read, list_missed_unswept
  query, documented payload build, watermark write, per-database
  lock) into the HA-free core (core/sweep.py), building each event
  through the shared events payload builder so the shape cannot
  drift; the integration's sweep.py becomes a thin shim that fires
  the returned events on hass.bus, keeping its signature.
- Admin trigger POST /api/v1/admin/missed-sweep: ONE clock read,
  ONE core call, each returned event published on the SSE stream
  through the existing publish_quest_missed helper; returns the
  fired count. Watermark makes a same-day rerun silent and a
  post-downtime run sweep the accumulated window once.
- Daily scheduler (api/scheduler.py) wired in the lifespan: reads
  day_rollover_time fresh each cycle, runs the sweep at the
  rollover, publishes on the app publisher, backs off and logs on
  failure, cancels cleanly on shutdown; injectable clock/sleep for
  tests.
- Tests: route trigger over a live uvicorn server with a live SSE
  stream (one transition per instance with documented fields,
  same-day rerun silent, post-downtime catch-up once, non-admin
  403 / absent 401) plus the scheduler rollover/cancellation test.

api/nestquest_core.py

@@ -198,6 +198,12 @@ core_dao_children = importlib.import_module(
 #: delegating.
 core_dao_rules = importlib.import_module(f"{_CORE_MODULE_NAME}.dao_rules")
 
+#: The HA-free missed sweep (``core.sweep.run_missed_sweep`` +
+#: ``SWEEP_WATERMARK_KEY``) the admin plane's trigger route calls and
+#: the daily scheduler runs — the ONE sweep policy the integration's
+#: bus shim shares.
+core_sweep = importlib.import_module(f"{_CORE_MODULE_NAME}.sweep")
+
 __all__ = [
     "core",
     "core_children",
@@ -218,4 +224,5 @@ __all__ = [
     "core_snapshot",
     "core_settings",
     "core_settings_store",
+    "core_sweep",
 ]