The Russian casualty rates (according to UKR, as ever) are rising quite steadily in this new phase of untrained or barely-trained conscripts being thrown into the meat grinder. 800 a day. It's horrific. Seems to mostly concentrated in the Donetsk region.
UKR also seems hesistant to go for a full on attack on Kherson. The Russians wouldn't hesistate to enact Scorched Earth on UKR territory even if they've proclaimed it part of Russia.
I don't think Ukraine is hesistant on Kherson.
Russia is, I suspect, thinking in set-pieces again. They're reinforcing Kherson, because they (I suspect) are planning on the idea that they can do a classic set-piece urban defence on it, withdrawing their better troops to the city while leaving expendable conscripts to act as a fighting rearguard to slow and attrit the Ukrainian advance.
But I don't think Ukraine is going to do that, for two main reasons.
One, urban combat is EXPENSIVE on the attacker, especially against what are likely to be well-prepared defensive positions and the best troops Russia has left.
Two, their strategy to date has been based on encirclement and logistics denial. We know Russia's logistics are in a parlous state, and quite easily disrupted by HIMARS from the western side of the Dnipro - Kherson could end up being the eastern end of a pocket which Russia would struggle to resupply. So they can move into just out of range of any Kherson-based artillery, dig in, and just sit there.
I wouldn't be surprised if there were some other attack to try and cut off the western side of the Russian-held ground, somewhere west of Zaphorhizhzhia, down to Melitopol, which could have a profound effect on Russia's supply situation in Kherson. We know that Ukraine are masters of the art of maskirovka (case in point: the Kharkiv attack), and all this movement around Kherson, while significant, could be a repeat of the "dead cat" operation they did prior to pushing east up there.
All wild speculation, of course, but I'm increasingly inclined not to underestimate the cunning and art of the Ukrainian approach to war - they seem positively allergic to doing it the Soviet way, while the Russians seem incapable of doing it any other way.