Is it obligatory to pay delayed Zakat in the original currency or in its equivalent value at the time it was due, taking into account the currency’s depreciation, and is it permissible to estimate the amount using a commodity other than gold to avoid usury?

If you have overdue zakat and the currency has depreciated, you are only obligated to pay the overdue amount. As for considering currency depreciation and compensating for the difference, this applies to debts between people according to some scholars, and this is what is issued as fatwa on this website. However, most scholars and the Islamic Fiqh Council have adopted the view that debts are repaid in kind, not in value, as long as the currency is still in circulation and has not been abolished. The Permanent Committee and Ibn Uthaymeen have issued fatwas to this effect, indicating that loans are repaid in kind without considering the difference in purchasing power. Although considering currency depreciation in the rights of people (inter-personal dealings) is valid, it is not obligatory for zakat and the rights of Allah. Nevertheless, doing so as a precaution is good. It is not obligatory to pay the excess in another currency.