Is testifying to something not heard directly, but rather conveyed by trustworthy individuals, considered a false testimony that necessitates expiation, given that the claimant is the one who sought the divorce and filed the case?

It is not permissible for a Muslim to bear witness except to what he knows and is certain of, based on the words of Allah Almighty: "except for those who testify to the truth, and they know" and "And we did not testify except to what we knew." Therefore, your statement, "I heard the wife telling her husband, 'Divorce me,'" when you did not actually hear her, is considered false testimony, which is one of the gravest sins. You should have only testified to what you actually heard and explicitly stated that you heard it from reliable sources and not directly from her. You must hasten to sincere repentance to Allah.