The spin dynamics of the layered square-lattice vanadate Pb${}_{2}$VO(PO${}_{4}$)${}_{2}$ is investigated by electron spin resonance (ESR) at various magnetic fields and at temperatures above magnetic ordering. The linewidth divergence towards low temperatures seems to agree with isotropic Heisenberg-type spin exchange suggesting that the spin relaxation in this quasi-two-dimensional compound is governed by low-dimensional quantum fluctuations. However, a weak easy-plane anisotropy of the $g$ factor points to the presence of a planar XY type of exchange. Indeed, we found that the linewidth divergence is described best by XY-like spin fluctuations which requires a single parameter only. Therefore, ESR-probed spin dynamics could establish Pb${}_{2}$VO(PO${}_{4}$)${}_{2}$ as the first frustrated square-lattice system with XY-inherent spin topological fluctuations.