Ukraine continues to take villages at Kharkiv, but they're reporting that many (all?) Russian troops have already retreated to the other side of the border - so Ukraine is punching at air. If Ukraine can undercut the troops and supplies heading into the Izyum offensive then it serves a strategic purpose - otherwise, not so much, they're just recapturing their own villages. Remains to be seen.

At Popasna, which is a topographic high point (and thus an excellent place to put artillery), they're currently shelling the Ukrainian strongpoints to their west and south rather than immediately marching onwards. Probably wise, don't wanna punch out too hard and form a hard-to-defend salient.

At Izyum, there's some issues due the forest line at Lyman (the area is a national park), but battles throughout the front.

I was watching Dreizin yesterday, who is among the more blatant chuds reporting on the war but does appear to have some useful military knowledge. He was talking about how Ukraine's buildings are built to be very sturdy, and the building and the people inside will survive most non-direct impacts from regular shelling. This therefore greatly slows down the offensive, as you need to go through each individual building to ensure that there aren't enemies in there who could shoot you and your tanks in the back while you're moving on, and it would be unnecessarily destructive to level every house in Ukraine. Every village in Ukraine is a potential fortification while it's occupied by enemy forces, and you can't just drive between the villages or you're then surrounded, not even to mention how you're gonna get vulnerable supplies through.