Is a sister's words about her friend, who did not inform her of her marriage, considered backbiting (gheebah), and is seeking forgiveness (istighfar) and repentance (tawbah) sufficient to erase the sin of backbiting, and what is the interpretation of the "bankrupt person" hadith in this context?

Gheebah (backbiting) is mentioning about your brother what he dislikes of his flaws, when those flaws are actually in him. If they are not in him, then it is slander. The punishment for the backbiter is severe in this world and the hereafter. Merely knowing that your friend is getting married and she has not told you or your other friend is not considered backbiting. Seeking forgiveness for your friend and praying for repentance are good deeds. As for the forgiveness of sins, that is among the matters of the Unseen.