We use x-ray spectroscopy at the Ir L3/L2 absorption edge to study powder samples of the intercalated honeycomb magnet Ag3LiIr2O6. Based on x-ray absorption and resonant inelastic x-ray scattering measurements, and exact diagonalization calculations including nearest-neighbor Ir-Ir electron hopping integrals, we argue that the intercalation of Ag atoms results in a delocalized electronic structure with enhanced Ir-O hybridization, departing from the local relativistic jeff = 1/2 state. We find that the relative orbital contribution to the magnetic moment is increased and the magnetization density is spatially extended and asymmetric in this hybridized state. Our results confirm the importance of metal-ligand hybridization in the magnetism of transition metal oxides and provide empirical guidance for understanding the collective magnetism in intercalated honeycomb iridates.