Should zakat be paid for previous years of debt, or to settle the debts of people first, given that the available amount is not sufficient for both?

The zakat that became obligatory upon you is not waived by debts you incurred after its obligation. If the wealth is insufficient for both zakat and debt repayment, then zakat must be prioritized. The right of a human being is not given precedence over the right of Allah, unless the person is under legal interdiction. In that case, the right of the human being is prioritized, unless the zakat is tied to the asset itself, in which case it is always prioritized.