Is the Hadith narrated by Muslim concerning the man who has intercourse with his wife and then becomes lazy, authentic, or are there defects in its chain of transmission (sanad) and text (matn), and does it contradict other Hadiths?

This hadith was narrated by Muslim, and there is weakness in one of its narrators, but Iyad was not alone in narrating it; he was corroborated. Abu Al-Zubayr was a mudallis (one who practices tadlis - concealing the identity of a sheikh or the fact that he did not hear a hadith directly from him) in it and did not explicitly state hearing it, but Al-Nawawi and Al-Hafiz Maghlatay clarified that what is in the Two Sahihs (Bukhari and Muslim) from mudallisun via ananah (narrating with "on the authority of") is considered to have established hearing from another source, and indeed, he explicitly stated hearing it in other narrations. Al-Albani authenticated it as mawquf (stopped) on Aisha.

As for the jurisprudence of the hadith: Merely mentioning sexual intercourse is not considered divulging a secret between spouses, unlike mentioning the details. If there is a benefit or advantage derived from mentioning it, then there is no dislike in doing so. As for the wisdom of the Prophet (peace be upon him) in informing about himself, it was for the sake of greater clarification, to emphasize the ruling, and to remove doubt, similar to the impact of his action in the Treaty of Hudaybiyyah. As for what was narrated from Aisha, it was a clear answer to a matter about which the Companions differed concerning the obligation of ghusl without ejaculation, and that was to resolve the disagreement and doubt.