What is the ruling on leading a congregation in the mosque without wearing an abaya, and what is the evidence for that?

For the prayer of the Imam, the congregant, and the individual to be valid, covering the 'awrah (private parts) is a prerequisite. This refers to what must be covered and whose exposure is deemed unsightly, based on the Almighty's saying: "O Children of Adam, take your adornment at every masjid." And based on the Prophet's (peace be upon him) saying: "Allah does not accept the prayer of a menstruating woman unless she wears a head covering (khimar)." If this condition is met, then wearing an abaya is not a prerequisite for imamate, nor is there any evidence for the desirability of the Imam distinguishing himself from the congregants in dress.