Or enforce cession through forcing a surrender, I suppose, if that distinction actually matters to anyone.
I don't have a good read on Putin or his motivations. My naïve take on the situation is that attempting to claim all of Ukraine, even after a protracted (to the extent of being frankly embarrassing for Russia) war, would engender so much hostility on the world stage as to make it not nearly worth the benefit. But how much will they take? Is Kharkiv likely to fall under Russian rule?
Kharkiv is held by the Ukrainians, so no, it won't go to Russia. But you'll see that Ukraine won't join NATO or the EU. Essentially 21st century Ukraine will be like a 20th century Finland. A neutral state.