  We consider dressing of excitonic properties by strongly correlated electrons
in gate controlled twisted homo-bilayer heterostructures. The combined effect
of the moir\'e potential and the Coulomb interaction supports the formation of
different strongly correlated phases depending on the filling, including
charge-ordered metals or incompressible insulators at integer occupation. The
coupling between excitons and electrons results in a splitting of the excitonic
resonance into an attractive and a repulsive polaron peak. Analyzing the
properties of the exciton-polarons across the different phases of the system,
we reveal a discontinuous evolution of the spectrum with the formation of a
double-peak structure in the repulsive polaron branch. The double-peak
structure emerges for non-integer fillings and it is controlled by the energy
separation between the quasi-particle states close to the Fermi level and the
high-energy doublons excitations. Our results demonstrate that exciton-polarons
carry a clear hallmark of the electronic correlations and, thus, provide a
direct signature of the formation of correlation driven insulators in gate
controlled heterostructures.
