Does one sin if they intended to fast a supererogatory fast then broke it for an invitation to a meal, and are they required to make up that day?

A Muslim is permitted to break a voluntary fast; in fact, it is recommended for him to complete it if there is no excuse. Several hadiths indicate this, including the hadith of Aisha (may Allah be pleased with her) that the Prophet (peace and blessings be upon him) broke a voluntary fast when Hays was presented to him, and the hadith of Umm Hani that the Prophet (peace and blessings be upon him) said: "The one observing a voluntary fast is his own master: if he wishes, he fasts, and if he wishes, he breaks his fast."