What is the ruling on the prayer of one who, as Imam, forgot a prostration before the Tasleem, whereupon the congregants alerted him, and he then completed the prostration of forgetfulness and then said the Tasleem, and they requested that the entire prayer be repeated—does he repeat it with them or not?

Prostration (Sujud) is a pillar (rukn) that cannot be compensated for by the prostration of forgetfulness (sujud al-sahw). Therefore, the Imam should have compensated for the forgotten prostration and what followed it, then performed the prostration of forgetfulness after the salutation (taslim). If he did not do that, his prayer is invalid. The congregants should have compensated for the prostration and what followed it, and performed the prostration of forgetfulness if the interval was not prolonged, because a rectified prayer is better than repeating a new prayer. What you did is incorrect. You should have performed the omitted prostration after the Imam's salutation, then prostrated for forgetfulness, or repeated the prayer with them. If you did not do that, you must promptly repeat the prayer, because omitting a pillar invalidates the prayer.