  Magnetic adatoms on surfaces are exchange coupled to their environment,
inducing fast relaxation of excited spin states and decoherence. These
interactions can be suppressed by inserting decoupling layers between the
magnetic adsorbate and the metallic substrate. Using low-temperature scanning
tunneling microscopy and spectroscopy, we investigate the magnetic properties
of single Fe atoms on Au(111) covered by a monolayer of MoS$_2$ and explore the
influence of the moir\'e structure on the spin excitation spectra. Fe adatoms
absorbed at minima of the moir\'e structure exhibit almost pure inelastic spin
excitations. Kondo correlations develop for adsorption sites off the moir\'e
minimum, culminating in fully developed Kondo resonances on moir\'e maxima. The
increase in Kondo correlations is accompanied by a decrease in the single-ion
anisotropy, which we rationalize by poor-person's scaling. Local variations in
the tunneling spectra indicate pronounced interference between tunneling paths
involving the spin-carrying orbitals and a hybrid Fe-S orbital, which forms
despite the nominally inert nature of the terminating S layer.
