Show last listing update time next to connection status in header

Add last_updated timestamp to /api/status endpoint by querying
MAX(last_seen) across both listing tables. Display it in the
HealthIndicator as relative time (e.g. "2h ago") with full
date/time in the tooltip on hover.

tests/integration/test_api.py

@@ -16,7 +16,8 @@ class TestStatusEndpoint:
         """Test that status endpoint returns OK status."""
         response = await async_client.get("/api/status")
         assert response.status_code == 200
-        assert response.json() == {"status": "OK"}
+        assert response.json()["status"] == "OK"
+        assert "last_updated" in response.json()
 
 
 class TestListingEndpoint: