BAI-3: harden live readiness diagnostics

Co-authored-by: multica-agent <github@multica.ai>

app/backend/features/system/routes.py

@@ -1,20 +1,12 @@
 from __future__ import annotations
 
-from datetime import datetime
 from http import HTTPStatus
 
 
 class SystemRoutesMixin:
     def _handle_system_public_get(self, parsed) -> bool:
         if parsed.path == "/api/health":
-            self.send_json(
-                {
-                    "ok": True,
-                    "storage": "sqlite",
-                    "account_required": True,
-                    "time": datetime.now().astimezone().isoformat(timespec="seconds"),
-                }
-            )
+            self.send_json(self.application_service.health_status())
             return True
         return False