A measurement of the Z$\gamma$ production cross section in proton-proton collisions at a center-of-mass energy of 13.6 TeV is presented. Data corresponding to an integrated luminosity of 34.8 fb${}^{-1}$, collected by the CMS experiment at the LHC in 2022 are used. Events with an oppositely charged pair of muons or electrons, with an invariant mass corresponding to a Z boson, together with an isolated photon are selected. The measured fiducial cross section for the combined electron and muon channels is 1.896 $\pm$ 0.033 (stat) $\pm$ 0.05 (syst) $\pm$ 0.006 (theo) pb, in agreement with the standard model prediction of 1.922 $\pm$ 0.094 pb. Constraints on neutral triple gauge couplings generated by dimension-8 operators in a recently proposed effective field theory framework are determined for the first time.