Fortunately, much progress has recently been achieved on both experimental and modeling sides. Improved operando measurement setups and subsequent data analyses provide more and increasingly accurate atomic-scale observables. Here, we illustrate this by now achievable widerange q-vector in situ XRR measurements in a tailored reactor setup that provide the adsorption height of a Gr monolayer above the liquid Cu catalyst (the so-called "gap") at unprecedented accuracy. On the modeling side, the advent of machine learning (ML) potentials constitutes a breakthrough . Trained with first-principles data, these ML surrogate models enable atomistic simulations and sampling comparable to classical force fields while reliably propagating the first-principles predictive quality even to the reactive surface chemistry characteristic for growth at liquid catalysts. Here, we exploit this novel methodology to quantitatively determine the "gap" and compare it to the experimental reference. Further, we also exploit the low computational demand and high data efficiency of the approach to train ML surrogate models with data calculated by different DFT functionals. This provides an unprecedented means to directly assess how much the functional uncertainty propagates to the "gap" and other literature observables for liquid Cu. Intriguingly we find only a low sensitivity and, furthermore, a clear correlation to easily accessible crystalline descriptors. This establishes firm guidance for choosing DFT functional in future first-principles ML surrogate-based mechanistic studies for catalysis at liquid metal surfaces.