feat: show update service status in UI

backend/update.py

@@ -220,3 +220,35 @@ def get_logs(settings: Settings, limit: int = 200) -> List[Dict[str, Any]]:
         except json.JSONDecodeError:
             continue
     return entries
+
+
+def get_service_status(settings: Settings) -> Dict[str, Any]:
+    base_url = settings.update_service_url.rstrip("/")
+    if not base_url:
+        return {
+            "url": "",
+            "reachable": False,
+            "status_code": None,
+            "error": "update service url not configured",
+            "checked_url": "",
+        }
+
+    check_url = base_url
+    try:
+        with httpx.Client(timeout=3.0) as client:
+            response = client.get(check_url)
+        return {
+            "url": base_url,
+            "reachable": True,
+            "status_code": response.status_code,
+            "error": None,
+            "checked_url": check_url,
+        }
+    except Exception as exc:
+        return {
+            "url": base_url,
+            "reachable": False,
+            "status_code": None,
+            "error": str(exc),
+            "checked_url": check_url,
+        }