  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.
