Ashtavakra describes the dissolution of the world: to the man who has realized the self, the visible world does not exist at all
The claim isn't that perception stops but that the world loses its status as something existing independently alongside the self, a position later Vedanta would call mithya.
Taken out of context, "the world does not exist at all" sounds like a claim that the realized person stops perceiving cities, bodies, and objects, but nothing else in the Gita supports that reading — Janaka continues to rule, converse, and act throughout. What dissolves is the world's status as an independently existing reality alongside the self; later Advaita Vedanta developed precise vocabulary for exactly this middle position, calling the world mithya, neither simply real like the self nor simply unreal like a pure fiction, but dependently real, the way a reflection is dependently real relative to a mirror. Chapter 5, opening with this claim, begins a run of verses using analogies of mistaken perception, a shell taken for silver, a rope taken for a snake, to make the point more concretely: what disappears upon realization is not the perceived object but the false additional belief about what kind of thing it is. This chapter's argument depends on everything built up through the ocean imagery of chapter 4: if the world was never anything but the self to begin with, "dissolution" simply names accurate seeing, not a change in what's there to be seen.
The technical term mithya, central to later classical Advaita Vedanta associated especially with Shankara and his successors, gives precise philosophical shape to the kind of claim Ashtavakra makes more suggestively here through imagery.
Ashtavakra Gita