We use x-ray spectroscopy at Ir L$_3$/L$_2$ absorption edge to study powder samples of the intercalated honeycomb magnet Ag$_3$LiIr$_2$O$_6$. Based on x-ray absorption and resonant inelastic x-ray scattering measurements, and exact diagonalization calculations including next-neighbour Ir-Ir electron hoping integrals, we argue that the intercalation of Ag atoms results in a nearly itinerant electronic structure with enhanced Ir-O hybridization. As a result of the departure from the local relativistic $j_{\rm eff}\! = \!1/2$ state, we find that the relative orbital contribution to the magnetic moment is increased, and the magnetization density is spatially extended and asymmetric. Our results confirm the importance of metal - ligand hybridazation in the magnetism of transition metal oxides and provide empirical guidance for understanding the collective magnetism in intercalated honeycomb iridates.
