What is the ruling on supplicating for a specific person, such as a king or president, and mentioning his name in the mosque? And why did scholars dislike that, as Sheikh Yusuf Al-Qaradawi mentioned?

It is permissible to supplicate for a Muslim. Supplicating for the ruler to be righteous is permissible because his righteousness entails the well-being of the subjects. Supplication for the ruler has been reported from the Salaf. As for supplicating for the ruler by name and from the minbar, scholars have differed on its permissibility, with some deeming it permissible and others reprehensible. The reason for reprehensibility, according to those who hold this view, is that it is an innovation. It is not appropriate to supplicate for a long life for an oppressor; rather, one should supplicate for his rectification and similar matters.