What is the ruling on one who does not forgive a Muslim who has apologized for a mistake he committed, and what sin results from that, and how is it expiated? And how should the behavior of the one who erred towards people be, and what is the fate of one who does not offer an apology or compensate for the harm?

Accepting an apologizer's excuse and forgiving a wrongdoer are among the great virtues of a believer. This is indicated by the Almighty’s saying: "And that you pardon is nearer to righteousness" (2:237), and "Let them pardon and overlook. Would you not like that Allah should forgive you?" (24:22). The wrongdoer should hasten to apologize and seek forgiveness to remove hatred and achieve harmony. They should choose the most upright way to apologize by being sincere, truthful, and selecting the appropriate time and words. It is preferable to accompany the apology with a gift, praise, or supplication. As for the hadith mentioned in the question, it is weak and not authentic.