I don’t have a discount entry in my cart. It is not necessary to show the discount in the cart.
My discount code can be added to each order. There will be validation at checkout that targets specific customer segments that First_order_date IS NULL. At checkout, after entering your email, Shopify will automatically reject the code for emails from which a purchase has already been made.
Therefore, it is important that the code is active immediately after entering checkout. How and where it will be added does not matter. Before proceeding to checkout, the user does not need to know about it.