[SEARCH-001] Search: Product search bar with live filtering

## Overview
Add a search bar to the header that supports live keyword search across products, with results updating as the user types.

## Acceptance Criteria
- [ ] Search input visible in the header on all pages
- [ ] Debounced live search (300ms) — results appear in a dropdown while typing
- [ ] Results show: product emoji, name, category, and price
- [ ] Clicking a result navigates to the Product Detail Page (#4)
- [ ] "See all results" link opens a full-page `/search?q=` results page
- [ ] No results state with a helpful message
- [ ] Search results are filterable and sortable on the full results page (price asc/desc, rating)
- [ ] Recent searches stored in `localStorage` (up to 5, clearable)
- [ ] Keyboard navigation in the dropdown (↑↓ to move, Enter to select, Esc to close)

## Technical Notes
Phase 1: client-side filtering over the product catalog JSON.
Phase 2 (post-MVP): server-side search with Elasticsearch or similar.

## Depends On
- #4 PDP-001 — search results must link to a complete product detail page

## Blocks
- #23 PERF-001 (search index optimization is part of performance work)