Does a slight swaying from side to side while reciting the Qur’an have a basis in religion, and what is the ruling on the prayer led by an Imam who does so?

Shaking and swaying during the recitation of the Quran, whether in prayer or otherwise, has no basis in Islamic law. What is recommended during recitation is tranquility and solemnity. The slight swaying of the Imam, if customary, does not invalidate the prayer, and prayer behind him is valid. However, it is advisable to abandon this practice.