First of all, if anyone tell you they have eliminate 200 tanks and 3000 soldier in 4 days, you probably need to treat this news with a serious grain of salt. This is NOT world war 2. If Ukraine did lose 200 tanks and 3000 soldiers in just 4 days, Russian should have, and would have counter attacked and taken more Ukrainian land considering the entire offensive probably would not have 500 tanks and 20,000 soldier with 5 to 6 Brigade, Russia should be at Mykolaiv by now if the Ukrainian had taken those loss.
Second of all, it does not really take a military genius to see Ukraine is playing the long game, and from a Trained Military Officer perspective, the way Ukrainian attack along the line of Russian Ground Line of Communication (The Bridges, The Ammo dumps and HQ/Communication), it shows Ukraine DO NOT want a frontal attack on Kherson, instead the Ukrainian wanted to cut off Russian line of retreat and threaten Russian rear, not saying the Ukrainian will be able to do that or not, that's depends on whether or not the Ukrainian can take E58 and cut off Russian Position in Kherson from Crimea, if they can do that, then it's game over or Russia, but that did show Ukraine is not going to have a fixed assault on a static front, which mean the 200 tanks and 3000 soldiers loss highly likely a myth.
Thirdly, Russian media themselves had admitted that they had lose several positions, albeit they said they loss those position in exchange with the aforementioned Ukrainian Casualty. Amongst those Russian admitted losing are 2 very important cities are Tomyna Balka and Velyka Kostromka, both are essential for Russia to hold Kherson. Tomyna Balka overlook T-1501 highway, it basically the entrant of Kherson City from the West, losing Tomyna Balka means they have lost the front door and the next step on Ukrainian agenda would be Bilozerka, which literally on the outskirt of Kherson City. Losing Velyka Kostromka means losing access to P47 Highway, which basically serve 2 purposes for Ukraine. 1. It gives them a clear run to Nova Karkova, where the hydroelectric dam was and where it feed Crimea fresh water. 2. It P47 continue with M14, which is the other axis of Ukrainian advance, IF the Ukrainian can come down from P47 and E58 and link up with M14, that basically serve as Blocking Position to Kherson. Which mean Russia access to the rear will be blocked off.