Is the imam's supplication for the sick after prayer and the congregants' saying "Amen" to the supplication considered an innovation, bearing in mind that the mosque is the only gathering place for Muslims?

Allah has commanded us to supplicate and encouraged it. Supplicating for the sick is recommended, whether the supplication is individual or collective. Prophetic supplications for the sick have been reported. As for collective supplication after the prescribed prayers, it is not legislated, due to the absence of legal evidence for it. However, if it happens occasionally, there is no harm. It is sufficient for the Imam to urge the congregants to supplicate for the sick and visit them.