The ISW’s “analysis” leaves much to be desired. My assessment (from looking at information sources from BOTH sides - I know, that’s a novel concept here)) is that the Russians are having “non-essential” civilians evacuate from the right bank of the river. That way they won’t have to resupply the civilians’ needs for survival. They’ll be able to focus solely on the logistics needed to support their military forces there. And they are substantially increasing their forces there.
If that were true wouldn't the barges headed to the right bank be loaded with trucks and soldiers and the empty barges headed the other way?