The nature of charge transport within a correlated background medium can be described by spinless fermions coupled to bosons in the model introduced by Edwards. Combining numerical density matrix renormalization group and analytical projector-based renormalization methods, we explore the ground-state phase diagram of the Edwards model in one dimension. Below a critical boson frequency, any long-range order disappears and the system becomes metallic. If the charge carriers are coupled to slow quantum bosons, the Tomonaga-Luttinger liquid is attractive and finally makes room for a phase separated state, just as in the t-J model. The phase boundary separating the repulsive from the attractive Tomonaga-Luttinger liquid is determined from long-wavelength charge correlations, whereas fermion segregation is indicated by a vanishing inverse compressibility. On approaching phase separation, the photoemission spectra develop strong anomalies.