Reason why Russia are retreating Kherson: It makes no sense to sacrifice their best units to try and hold onto a town where they run the risk of being cut off logistics supplies
Russian defensive works being built on the east bank of the Dnieper, facing Kherson. Those are already sometimes stretching up to 18km in depth in some parts.
The deal with Kherson: Some of Russia's best troops are on the west bank of the Dnieper. We're talking best trained (pre-war) and by now battle hardened if depleted. There are a fair few VDV units deployed there as well as units belonging to the 58th CAA. They've been fighting since day one of the conflict and they gave Russia its biggest successes in the war so far: Rush out of Crimea, advances to Energodar, Kherson, Nikolayev and Krivyi Rih. Basically the whole of Kherson Oblast and 70% of the Zaporizhzhia Oblast.
They've held ground (and withdrawn under pressure) better than other Russian outfits. However, with logistic lines across the Dnieper constantly targeted, they can't get the ammo they need in the face of another large Ukrainian offensive. They stalled the Ukrainians the last time and are inflicting losses on the AFU daily. But they don't get the tools needed to resist another large scale onslaught and are at risk of facing a slow attrition on the west bank of the Dnieper at best or being overwhelmed and cut off at worst.
It looks like they are being withdrawn and replaced by "lesser" units dedicated to cover their retreat. Using the Dnieper as a natural defensive barrier would make sense for Moscow. Although, if they give up Kherson (city) now, they're unlikely to ever retake it.
It makes no sense to sacrifice their best units to try and hold onto a town where they run the risk of being cut off. It's not of any strategic importance unless one wants to advance to Nikolayev and Odessa. Something the RF are unable to do in their current posture.
While pushing beyond Kherson made sense initially in order to prevent Ukrainian strikes on Crimea and on Russian positions on the east bank of the Dnieper, this no longer works.
As for the Ukrainians, retaking Kherson would give them a success to celebrate (taking lands is nice, taking a city is nicer!) And it would provide them with peace of mind and security as far as Nikolayev and Odessa are concerned. For them, too, the Dnieper could act as a natural defensive barrier: Take Kherson, "raise the drawbridge" and use the river as a wet moat.