Does listening to music or breaking an oath constitute disbelief (kufr)? And do the Hadith "He has no religion who does not keep his promise" and "Three types of people will have me as their opponent on the Day of Resurrection: a man who gives a promise in My Name then breaks it" apply to this case?

The denial of faith and religion in the hadith "He has no faith who has no trustworthiness, and he has no religion who has no covenant" is understood to mean the denial of the perfection of obligatory faith, not an expulsion from Islam. Betraying a trust and breaking a covenant are major sins, and whoever swears by Allah and then betrays is an adversary of Allah on the Day of Resurrection. Whoever breaks an oath must offer an expiation for the oath (feeding ten poor people, clothing them, or fasting for three days). As for "oath of contention" (like saying, "If I listen to music, I will fast the next day"), if one breaks it, they have the choice between fulfilling the vow or offering the expiation for an oath. If fulfilling the vow is impossible, then expiation is the solution. A believer must avoid sins without needing vows and oaths, strengthen faith through acts of worship, and beware of obsessive doubts.