I have a payment link from a payments handler (they don't have any integrations with any ecomm platform, yet) and was looking for a way to add this payment link to checkout.
Why? because I wanted to start selling sooner while I wait the long process of opening a business bank account in the UAE.
Shay from the Shopify team commented on a tweet that: "the checkout can only be customized if you are on the Shopify Plus plan. All our standard plans will not allow access to the checkout API to ensure the security of the checkout process."
So although I'm posting this as a question, I'm also posting as an answer.
If you're on the basic plan like me, you're out of luck in the payment link x Shopify dept. For everything else, there's MasterCard.