Correlated transition metal oxides, such as cuprates, nickelates, and manganites, are typically considered "bad metals", where high electromagnetic losses suppress the conventional plasmonic effects observed in noble metals, 2D electron gases, and graphene. Nevertheless, using mid-infrared near-field optical nanoscopy, we demonstrate the emergence of strongly laterally confined and long-propagating edge polaritons (EPs) of mixed phonon-plasmon nature at the boundaries between conducting and insulating regions in thin NdNiO₃ films, fingerprinted as a pronounced peak of the near-field signal phase. Our simulations reveal that the electromagnetic nature of the EPs depends significantly on the edge smoothness, being caused by a one-dimensional optical edge state (ES) at abrupt edges while being governed by the epsilon-near-zero (ENZ) absorption in the case of broad boundaries. Our findings highlight the critical role of nonlocal plasmonic effects in near-field imaging of phase-separated correlated oxides and open new avenues for infrared plasmonics in this family of materials.