Is the designer subject to sin or debt towards the client after the client refrained from paying for the book cover design, which was previously agreed upon, and the designer voluntarily reduced the amount to only the design value?

The agreement between you two is a manufacturing contract (Istisna'), which is a request to produce something not yet made, with specific specifications and materials provided by the manufacturer, in exchange for a price. It is not a condition for the capital to be seized at the contract assembly; rather, it may be paid in full, in part, or not at all until the manufactured item is delivered. If the manufactured item is delivered in accordance with the specifications, the procurer is obliged to accept it and pay the price. However, if it is not in accordance, he has the option to accept or reject it. If the design conforms to the agreed-upon specifications, the procurer is obligated to pay the full price of 1600, and you are obligated to deliver the design after printing it. It is permissible for you both to reconcile on the price of the design without printing it; otherwise, you must revert to the initial agreement.