CART-003: Cart API — backend integration for persistent cart and checkout

## Overview
Connect the client-side cart to a backend API for cart persistence across sessions and a real checkout flow. This ticket is currently **blocked** pending the backend team provisioning the Cart API endpoint.

## Acceptance Criteria
- [ ] Cart state is persisted to the backend on every add/remove action
- [ ] Cart is restored on page load if the user has an active session
- [ ] Checkout button initiates a real order creation via the Order API
- [ ] Error states handled gracefully (API timeout, out-of-stock)

## Depends On
- #34 (CART-002 — client-side cart state)

## Blocks
- #41 (ACC-005 — Wishlist: 'Move to Cart' action)
- #43 (PROMO-007 — Promotions Engine: requires real cart contents for discount eval)
- #46 (ORD-001 — Order Service: converts cart to order)

## Status
🔴 Blocked — waiting on backend API provisioning (3 weeks and counting)

No files, tests, or entry points are named. Start by resolving the blocked Cart API provisioning and reviewing dependency #34, then trace the client cart integration and Order API requirements. Done means persistence, session restoration, checkout order creation, and graceful timeout and out-of-stock handling meet the listed acceptance criteria.

Written by the indexing model from the issue text.