(ui) Add dashboard operational status summary

Make queued, running, warning, and failed run states more visible at the
top of the dashboard with contextual status summaries and highlighted
summary metrics.

Also show an all-clear message when configured hosts have no active or
problematic runs.

src/pobsync_backend/tests/test_views.py

@@ -84,6 +84,11 @@ class ViewTests(TestCase):
         self.assertContains(response, "running 1")
         self.assertContains(response, "warning 1")
         self.assertContains(response, "failed 1")
+        self.assertContains(response, "Operational Status")
+        self.assertContains(response, "1 failed run needs review.")
+        self.assertContains(response, "1 run completed with warnings.")
+        self.assertContains(response, "1 backup run in progress.")
+        self.assertContains(response, "1 backup run waiting for the worker.")
 
     def test_dashboard_renders_backup_trend_summary(self) -> None:
         self.client.force_login(self.staff_user)
@@ -148,6 +153,17 @@ class ViewTests(TestCase):
         self.assertContains(response, "No completed backup runs with stats yet.")
         self.assertContains(response, "growth estimates")
 
+    def test_dashboard_shows_all_clear_operational_status(self) -> None:
+        self.client.force_login(self.staff_user)
+        GlobalConfig.objects.create(name="default", backup_root="/opt/pobsync/backups")
+        HostConfig.objects.create(host="web-01", address="web-01.example.test")
+
+        response = self.client.get(reverse("dashboard"))
+
+        self.assertEqual(response.status_code, 200)
+        self.assertContains(response, "Operational Status")
+        self.assertContains(response, "No queued, running, warning, or failed runs.")
+
     def test_dashboard_surfaces_retention_warnings(self) -> None:
         self.client.force_login(self.staff_user)
         host = HostConfig.objects.create(