Going through step 4 on the app example it uses AppBridge.hostOrigin to return the store URL:

const data = { host: appBridge.hostOrigin, productHandle: handle.value || selectedProduct.handle, discountCode: discountCode.value || undefined, variantId: variantId.value, };

However per this issue, appBridge.host was not intended for part of the public API and now returns the admin URL and not store URL.

Would be good to have the example app updated to read the storefront URL.