Here is a guide on using checkout with the storefront api. If you were looking to have customer avoid hitting the webUrl entirely, it would require a special permission that is reserved normally for sales channels. It is recommended you use the Shopify Checkout for all transactions.
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I have read the checkout guide for the storefront API.
Is it possible to use other payment options within the API than credit card or the `webUrl`?
The "webUrl" returns a unique URL that you can use to direct customers to the Shopify checkout. This should allow you to take any supported payment methods for your shop.