On Store › Orders › New order, choose Not paid yet: send a payment link under Paid by. The order is created unpaid and its items are held for it. Magpie makes a payment link for the order's total on your Stripe account and emails it to the customer.
The order's page has a Payment link section to copy the link, email it again or make a new one. A link works for 24 hours; after that the order stays unpaid with its items held until you make a new link or cancel the order. When the customer pays, the order is marked paid, its items leave stock, and the customer gets the order confirmation.