(feature) Add staff-only service status API

Add /api/status/ for quick inspection of database backend, object counts, latest
backup run, and latest scheduler activity. Link it from the API index and reuse
schedule serialization between host summaries and status output.

Cover the endpoint with a focused API test and document the new status URL.

src/pobsync_server/urls.py

@@ -8,6 +8,7 @@ from pobsync_backend import api
 
 urlpatterns = [
     path("api/", api.api_index),
+    path("api/status/", api.status),
     path("api/hosts/", api.hosts),
     path("api/snapshots/", api.snapshots),
     path("api/runs/", api.runs),