Is it authentically reported from the Prophet (peace be upon him) that the Imam would pause at the end of the Friday sermon to allow the congregants time for collective seeking of forgiveness, as occurs by raising hands and supplicating silently?

If the questioner means seeking forgiveness for two minutes at the end of the second sermon, this has no basis, and what is prescribed is to establish the prayer immediately. However, if the questioner means seeking forgiveness between the two sermons after the Imam has sat down, there is no objection to it, especially since the hour of responsiveness (sa'at al-ijabah) on Friday is between the Imam sitting on the minbar and the prayer being concluded, according to a hadith (definition) in Muslim. Therefore, it is permissible for the congregants to seek forgiveness silently and individually at this time, but raising the hands in this position is not prescribed.