  The interplay of Coulomb and electron-phonon interactions with thermal and
quantum fluctuations facilitates rich phase diagrams in two-dimensional
electron systems. Layered transition metal dichalcogenides hosting charge,
excitonic, spin and superconducting order form an epitomic material class in
this respect. Theoretical studies of materials like NbS$_2$ have focused on the
electron-phonon coupling whereas the Coulomb interaction, particularly strong
in the monolayer limit, remained essentially untouched. Here, we analyze the
interplay of short- and long-range Coulomb as well as electron-phonon
interactions in NbS$_2$ monolayers. The combination of these interactions
causes electronic correlations that are fundamentally different to what would
be expected from the interaction terms separately. The fully interacting
electronic spectral function resembles the non-interacting band structure but
with appreciable broadening. An unexpected coexistence of strong charge and
spin fluctuations puts NbS$_2$ close to spin and charge order, suggesting
monolayer NbS$_2$ as a platform for atomic scale engineering of electronic
quantum phases.
