What's happening in Kherson oblast on the West side of the river is encouraging, and more a case of preparing the battlefield. I don't see however that Ukraine has yet the capabilities for actual offensive maneuvre warfare beyond that side of the Dnipro: This would take plenty of certain kinds of equipment (tanks) with respective ammo, some aerial capabilities (helicopters, planes, ARM), and most importantly enough soldiers and officers trained in combined arms maneuvre warfare of that kind. They may over time succeed in pushing the Russians back East, even contest the city of Kherson, but I do not see Ukraine establishing a bridgehead on the East bank and moving offensively from there.
I would guess the main short-term goal is to demonstrate that Russia can not hope to be secure in the territories they think they control, and hand them some sort of tangible defeat to challenge morale further.