Discount Code is hidden
To clarify - Product Builder Custom Products cannot be used alongside Shopify Discount Codes.
This is due to a Shopify Platform limitation - your Custom Products needs Shopify's Draft Orders functionality in order to work as expected, but as a design-choice on Shopify's side, the Draft Orders function overrides that of the Discount Code system.
The following FAQ can offer more context regarding this:
App Basics: Draft orders primer, when working with other apps
As the Shopify platform does not allow discount codes to be used in conjunction with their Draft Orders functionality, our hands as app developers are unfortunately tied on this.