Engineering the electrolyte microenvironment represents an attractive route to tuning the selectivity of electrocatalytic reactions beyond catalyst composition and morphology. However, harnessing the full potential of this approach requires understanding the interplay between voltage, electrolyte composition, and adsorbate binding within the electrical double layer, which is absent from the usual theoretical approaches. In this work, we apply a recently developed density functional theory (DFT)-continuum approach based on the effective screening medium method and reference interaction site model (ESM-RISM) to explore electrolyte effects with an enhanced description of the electrochemical interface. Applying this method to the binding of CO adsorbates in potassium-containing electrolytes on copper, a problem of direct relevance to CO2 electroreduction to value-added products, we show that the interdependence of voltage and pH leads to an unexpected change in adsorption site preference on Cu(001) terraces. Our findings highlight the often-overlooked importance of the electrical double-layer structure for predicting catalyst operation.