Does supplicating for forgiveness for someone I have cursed at absolve the sin of cursing them, as is understood from the Hadith: "O Allah, to any believer whom I have cursed, make that a means of drawing him closer to You on the Day of Resurrection"?

The fundamental principle for absolving oneself of the rights of others is by seeking their forgiveness or returning what is due to them. No one other than the Prophet, peace and blessings be upon him, can be compared to him, for he stipulated to his Lord that his cursing and reviling of people be a purification and a reward for them. As for others, cursing or reviling without just cause reverts to the one who utters it. Jurists have mentioned that if the right pertains to one's honor, then it suffices to supplicate for the person, belie oneself, and praise them.