How is the Hadith of Jabir, which narrates the Prophet's (peace and blessings of Allah be upon him) going to his wife Zaynab after seeing a woman, considered authentic, even though this action is private and it is inconceivable for the Messenger to disclose it to the Companions?

This hadith was narrated by Muslim, and the Prophet's actions (peace be upon him) were a clarification and guidance for what Muslims should do, teaching them through example and word. What transpired with him (peace be upon him) was not merely a recounting, but rather an act of legislation and discipline, and he (peace be upon him) is infallible. This meaning has been supported by Ibn al-Arabi, al-Nawawi, al-Manawi, and Ibn Muflih. Among what confirms this is the hadith of Abu Kabsha al-Anmari, in which the Prophet (peace be upon him) entered then exited after performing ghusl, and said: "So-and-so passed by me, and a desire for women entered my heart. So I went to one of my wives and had intercourse with her. Do likewise, for indeed, among your best deeds is coming to the lawful."