Does the husband's debt to his wife, who used her private funds to purchase something for herself, which he promised to repay, remain a trust upon him after the divorce (khulʿ) and her waiver of half of the deferred mahr, knowing that she forgot to claim it at the time?

If what the wife bought is outside the scope of obligatory maintenance, then it is a promise from the husband, and fulfilling it is recommended according to the majority of scholars, and obligatory according to the Malikis if the promised party entered into a commitment because of it, which seems to be the case in this matter. However, if the purchase falls within the scope of obligatory maintenance, then it is a debt owed by the husband that is not waived unless the wife voluntarily waives it. She has the right to demand it from the husband, and it is not waived by her waiving half of the deferred Mahr.