Is the zakat on gold calculated based on its value at the time the Hawl (lunar year) is completed, or at the time it is disbursed?

You erred by delaying the zakat (definition) from its due time, as long as there was an eligible recipient. It is not permissible to delay it unless the zakat payer cannot find any deserving individuals. You must repent for this.

It is necessary to know the weight of the gold upon which a year has passed. If it reaches 85 grams or more of pure gold, zakat becomes obligatory on it. The obligatory amount to be given is one-quarter of one-tenth (2.5%). The principle is that it should be given from the gold itself, and there is no need to know its value at that time.

However, if you wish to pay the value of what is due, that is permissible. In this case, its value at the time of payment, not at the time it became due, should be considered.