feat: enhance health check with application state and initialization status

apps/frontend/app/generated/api-client/api-client.ts

@@ -3,6 +3,7 @@ export namespace Schemas {
   export type AdminInitRequest = { password: string; setup_secret: string; username: string };
   export type HealthInfo = {
     errors?: (Array<string> | null) | undefined;
+    is_initialized: boolean;
     status: string;
     up_since: string;
     version: string;