Your gift card will be added under "Gift Cards" in your Fold account as soon as your payment is confirmed. For credit card and Lightning Network orders, this usually only takes a few seconds.
For BTC orders, your payment may take a few minutes until it is confirmed on the blockchain. When your order is complete, you will receive a notification in the app that your card is ready to use. It's unusual, but if you don't see your card show up after more than 20 minutes, please submit a support ticket. If your BTC send is confirmed after your invoice expires, your Fold account will be credited that BTC, which you can spend on a future order.