It is a PR victory too, yes. But that's mostly because the military victory here was so quick, so easy and so massive that it naturally makes for good PR. Winning all of Kharkov region in 3 days isn't merely a PR stunt, but it sure as hell is good PR.
Also how are they supposed to be cut off? Russians retreated from the region almost entirely. They didn't have the resources to mount a defence of territory they invested months to take, how are they supposed to retake it or cut Ukraine off from Kharkov region?