Is it permissible to pay zakat to settle a debt incurred by a family for renovating their guesthouse (diwan), given that their financial situation is moderate, and is settling a debt with one's own money considered charity?

Whoever appointed you to distribute zakat has entrusted you to disburse it to those who are eligible, without favoritism. It is permissible to pay off the debts of your indigent family members from it, or from your voluntary charity.