  Quantum spin systems with kinetic constraints have become paradigmatic for
exploring collective dynamical behaviour in many-body systems. Here we discuss
a facilitated spin system which is inspired by recent progress in the
realization of Rydberg quantum simulators. This platform allows to control and
investigate the interplay between facilitation dynamics and the coupling of
spin degrees of freedom to lattice vibrations. Developing a minimal model, we
show that this leads to the formation of polaronic quasiparticle excitations
which are formed by many-body spin states dressed by phonons. We investigate in
detail the properties of these quasiparticles, such as their dispersion
relation, effective mass and the quasiparticle weight. Rydberg lattice quantum
simulators are particularly suited for studying this phonon-dressed kinetically
constrained dynamics as their exaggerated length scales permit the
site-resolved monitoring of spin and phonon degrees of freedom.
