Add Zod validation on admin form with per-field errors + submitting state

## Goal
Validate the admin form with Zod, showing per-field errors only when touched (or on submit attempt), and disable the submit button while submitting.

## Acceptance criteria
- [ ] Form values validated against the Zod food schema
- [ ] Per-field error messages shown after touch / on submit attempt
- [ ] Submit button disabled while in flight
- [ ] Playwright test covers create, edit, and delete happy paths

Start by locating the admin form, the existing Zod food schema, and the current Playwright tests. Confirm validation timing, per-field messages, and submit-button behavior, then extend coverage to create, edit, and delete happy paths until all acceptance criteria pass.

Written by the indexing model from the issue text.