Russia is in Lyman today. Last city on this side of the river.
I heard fairly recently (last 12 hours or so) they were on the northern outskirts, and pounding the town. Zalenskyy finally told his guys to get out of Sievierodonetsk. But when they do, a large part of the Luhansk will be taken by the Russians.
Kharkiv, by the way, is about 60 miles northwest from the Donbas.