CART-002: Add-to-cart — client-side cart state with item count badge

## Overview
Add client-side cart functionality. Users can add products to a cart that persists in memory. The cart icon in the header shows the total item count.

## Acceptance Criteria
- [ ] Clicking 'Add to Cart' adds the item to the in-memory cart array
- [ ] Adding the same item twice increments the quantity
- [ ] The cart badge in the header reflects the total item count
- [ ] A toast notification confirms the item was added

## Depends On
- #33 (CART-001 — Product catalog)

## Notes
Checkout (payment/persistence) is out of scope for this ticket — that is CART-003.

Start by reviewing issue #33 and the product catalog's Add to Cart entry point, then locate the header cart icon and badge. Implement the in-memory cart behavior and toast described in the acceptance criteria, and verify duplicate additions update the total item count while checkout remains out of scope.

Written by the indexing model from the issue text.