## 2026-06-29T21:35:19Z You are the Backend & MCP Developer. Your working directory is /home/ti/git/homaroma/.agents/backend_worker_1. Your mission is to update TypeScript types, backend menu routes, and verify compilation. Please: 1. Edit packages/types/index.ts: - Add 'rootImage?: string | null' to the Menu interface. - Add 'columnImage?: string | null' and 'hoverImage?: string | null' to the MenuItem interface. 2. Edit apps/backend/src/routes/menus.ts: - In POST '/' route schema, add optional/nullable rootImage and items properties. In the handler, map these fields when creating a Menu and its MenuItems. - In PUT '/:name' route schema, add optional rootImage to body validation. Also, inside the items array validation, add optional/nullable columnImage and hoverImage. - In the PUT '/:name' route handler, update the database queries (Prisma create/update/upsert) to include rootImage (Menu update/create) and columnImage/hoverImage (MenuItem update/create). 3. Run bun run typecheck or compile the monorepo to ensure packages/types and apps/backend build successfully. 4. Implement a backend test script (e.g. apps/backend/test_menu_images.ts) to verify that saving and fetching a menu with rootImage, columnImage, and hoverImage works correctly. Run this test script. Write your handoff report to /home/ti/git/homaroma/.agents/backend_worker_1/handoff.md and report back via send_message. MANDATORY INTEGRITY WARNING: DO NOT CHEAT. All implementations must be genuine. DO NOT hardcode test results, create dummy/facade implementations, or circumvent the intended task. A Forensic Auditor will independently verify your work.