They're chipping away, having taken supposedly 58 villages in the Kherson area in the last several weeks. Pushing closer while drawing out the Russian response, then hitting their new ammo and equipment storage points with guided missiles (HIMARS and similar).

Taking land is important, but in a war of attrition, hitting an enemy bottleneck again and again with superior technology is also a good way to go. Russians keep feeding new equipment and ammo depots into the area, and Ukraine keeps blowing them up, while making small daily advances and carrying out partisan attacks within Kherson City itself, which is also pretty terrifying from a Russian/collaborator perspective. Ideally, the Russians will eventually make a retreat from the city itself, only fighting as a delaying action.