Depth-dependent electronic states of a prototypical strongly correlated Fe3O4 thin film across the Verwey transition temperature (TV ~125 K) were investigated by hard x-ray photoemission spectroscopy (HAXPES) combined with x-ray total reflection (TR). We found that the Fe 2p HAXPES spectral shapes strongly depend on the effective inelastic mean-free-path (eff) regardless of temperature (T). Particularly, the shoulder structure located at the lower binding energy side of the Fe 2p3/2 main peak becomes more pronounced with increasing eff, (i.e., increasing bulk sensitivity), indicating a significant difference in the electronic structures between the surface and deeper regions of the film. This trend coincides with the increase of the density of states near the Fermi-level (EF) for larger eff, suggesting the contribution of non-local screening effects. While the valence band spectra show a clear metal-to-insulator transition across TV, the Fe 2p core-level HAXPES and the magnetic circular dichroism profiles for large eff are almost independent on T. This behavior suggests that the average valence of the B-site Fe species is maintained at 2.5+ across TV. Comparison with the configuration interaction theory based on the cluster model calculations emphasizes the importance of non-local screening effects in the Fe 2p spectral shapes. Our results demonstrate that HAXPES combined with TR is a powerful technique for probing systematic depth-dependent electronic states. By providing this systematic dataset from the surface to deeper regions, this work serves as a reliable benchmark for the research field.