Charge the account's saved card for this cart and create the order, with no person in the loop.

Preconditions: the cart is open, its quote is ready, it has a ship_to and a shipping_option_id, a nonblank customer_phone or ship_to.phone for delivery contact, and the account has a card on file (GET /v1/account, saved on the website's account page) or the request names a Stripe PaymentMethod. The charge is the cart's totals.amount_total_cents. New payments require at least $32 before sales tax, including shipping and production surcharges (409 minimum_order_not_met). On success the cart becomes checked_out and the response carries order_id. An uncertain result returns 202 with status processing; a durable worker retries order creation with the same payment. A failed handoff returns 502 order_creation_pending while recovery continues; retry this cart, not a new payment. Timeouts never trigger automatic refunds. Retrying a paid cart returns the existing payment.