I'm curious on how the Smoothness in the Interval section of Pixsort works technically, looks like a blur somewhere in the buffer process? Or is it based on a lower res image to sort less precisely?

Before sorting, a sort of threshold-mask is done to determine where pixel-sorting is allowed to take place. The smoothness parameter will do an average/blur of this threshold-mask to reduce the high frequency details and simplify the regions where pixel sorting is allowed to take place!