There seems to be some support for providing a discount code or coupon upon payment, but I can’t find any option to generate such coupons in the Merchant backend UI.
Is this currently an API only feature or not yet implemented in general?
This is a forthcoming feature. While the merchant backend supports it, support in the wallets is still spotty (best on Android) and also not yet ready in the backend UI (that will likely take much longer). Right now, this is on the roadmap for GNU Taler v1.6.