We present a new operational framework for studying "superpositions of spacetimes," which are of fundamental interest in the development of a theory of quantum gravity. Our approach capitalizes on nonlocal correlations in curved spacetime quantum field theory, allowing us to formulate a metric for spacetime superpositions as well as characterizing the coupling of particle detectors to a quantum field. We apply our approach to analyze the dynamics of a detector (using the Unruh-deWitt model) in a spacetime generated by a Banados-Teitelboim-Zanelli black hole in a superposition of masses. We find that the detector exhibits signatures of quantum-gravitational effects corroborating and extending Bekenstein's seminal conjecture concerning the quantized mass spectrum of black holes in quantum gravity. Crucially, this result follows directly from our approach, without any additional assumptions about the black hole mass properties.