Adsorption energy distributions (AEDs) have emerged as a powerful and increasingly adopted descriptor for catalytic performance in high-entropy alloys and, more recently, in conventional metallic alloy nanocrystal catalysts. By accounting for diverse adsorption sites and crystallographic facets, AEDs more fully represent nanoparticle-based catalytic surfaces and show strong promise for accelerating rational design and discovery of heterogeneous catalysts, especially for CO₂ hydrogenation. However, previous high-throughput screenings have not provided simultaneous facet-level insight into catalytic activity, product selectivity, and thermodynamic stability. Here, we implement and extend the AED framework to individual crystallographic facets, combining facet-resolved adsorption fingerprints with Wulff-derived facet abundances and an interpretable latent-space analysis of C1-product selectivity. We employ universal machine-learned force fields trained on Open Catalyst Project data to compute adsorption energies across 226 experimentally observed metals, binary alloys, and previously unexplored ternary alloys, encompassing ~1.4 million adsorption configurations on >2,600 crystallographically distinct surfaces. Using distribution-based similarity analysis and principal component analysis of AED moments, we identify composition-facet combinations with adsorption landscapes associated with activity and qualitative selectivity trends toward methanol, methane, formic acid, and CO. Our framework links surface structure to adsorption-based catalytic trends, providing experimentally testable composition-facet candidates for further investigation and validation.