What is the wisdom behind the Imam's turning to face the congregation after concluding the prayer? And does the statement that this is permission to leave the mosque have any basis in Islamic law, or is it merely a Sunnah?

It is Sunnah for the Imam to face the congregants after the prayer, as this has been reported from the Prophet, may Allah’s peace and blessings be upon him. This act of facing has multiple benefits, including teaching the congregants, informing those who enter that the prayer has concluded, and removing haughtiness and pride from the Imam towards the congregants. It is disliked for the Imam to prolong facing the Qiblah after the prayer; the Sunnah is that he should only sit for the duration of the remembrance (dhikr) reported from the Prophet, may Allah’s peace and blessings be upon him. It is Sunnah for the congregant not to depart until the Imam turns away from the Qiblah, based on the Prophet’s saying, may Allah’s peace and blessings be upon him: "Indeed, I am your Imam, so do not precede me in bowing, nor in prostrating, nor in standing, nor in departing." However, if the Imam prolongs his sitting while facing the Qiblah, it is permissible for the congregant to depart.