CART-001: Product catalog — browsable storefront with category filtering

## Overview
Implement the public product catalog page. Users should be able to browse all products and filter by category (phones, audio, wearables, accessories).

## Acceptance Criteria
- [ ] Product grid renders all products from the catalog data
- [ ] Category filter buttons update the visible products without a page reload
- [ ] Each product card shows: image placeholder, name, category, rating, price, and an Add to Cart button
- [ ] Filter state persists if the user navigates back to the catalog

## Notes
This is the foundation of the storefront. All other product-facing features depend on this.

No files, tests, or entry points are named; first inspect the repository structure and find the storefront entry point and catalog data. Implement the catalog page, category filtering, product-card fields, Add to Cart controls, and back-navigation filter persistence, then verify each acceptance criterion manually.

Written by the indexing model from the issue text.