What is the ruling on verbally abusing someone loudly at home without anyone hearing, and is it recorded as a sin, based on the Hadith: "Indeed, Allah has pardoned for my Ummah whatever they speak to themselves about, as long as they do not act upon it or speak of it"?

Abusing and cursing a Muslim is not permissible; it is an act of wickedness (fisq) and is forbidden by the consensus of the Ummah. As for cursing a Muslim in their absence, it is a form of impermissible backbiting (gheebah). If you uttered the abuse, you have fallen into sin, and you must repent to Allah and seek forgiveness from the one you backbit. However, mere self-talk does not apply to your situation.