What is the ruling on the prayer of the Imam and the congregants if the Imam prayed with ablution in which he did not remove his socks, which he had put on without being in a state of purity, and he remembered this during the prayer but did not withdraw from it?

Your prayer with that ablution is invalid, and you must exit the prayer immediately upon remembering the defect in your ablution. It is permissible for the congregants to put forward someone to complete their prayer with them. As for the prayer of the congregants, it is valid based on what some scholars have favored.