As far as I know, legislatures have independent power. I'd have to read GA constitution and more on GA state to get details. Governors generally have the power to call legislatures into session for issues that the Governor deems warrant doing so, but as I say a tthe start, legisltures have independent power. They just don't want to be accountable.
I don’t want to believe that the GA legislature is too cowardly to do anything to make the runoff fair, but how could I be too surprised if they act like politicians?