What is the ruling on someone who vowed to donate a specific amount of money after committing a sin, then became unable to pay the amount, and is fasting sufficient as a substitute for that?

A vow made in a fit of anger or obstinacy (Nathr al-Lajaj or al-Ghadab) does not necessitate fulfillment. Rather, one has the choice between fulfilling it or offering an expiation for an oath (kaffarat yamin). This is the view of the Shafi'i school, the well-known position of the Hanbali school, and one of the two narrations from Abu Hanifa. Therefore, there is no harm in offering an expiation for an oath. One must be wary of sins, hasten to sincere repentance, and take the necessary steps to abandon them.