What is the Messenger of Allah's ﷺ guidance regarding the two Friday sermons, and with what did he conclude them?

No authentic Hadith states what the Prophet, peace and blessings be upon him, used to say at the end of the two Friday sermons. However, a weak Hadith reports that he used to seek forgiveness for believing men and women every Friday, and another weak narration states that this seeking of forgiveness was at the end of the second sermon. Scholars have recommended concluding with seeking forgiveness, citing the actions of Ibn al-Qayyim, al-Nawawi, and al-Shuraim, as well as by analogy to the supplication for expiation of the مجلس (gathering), and based on what has been narrated from the Salaf, among them Abu Bakr al-Siddiq.