We stress that the limitations on one of the results of our paper [R. Goerlich et al., Phys. Rev. E 106, 054617 (2022)2470-004510.1103/PhysRevE.106.054617], which are mentioned in the preceding Comment [A. Bérut, preceding Comment, Phys. Rev. E 107, 056601 (2023)10.1103/PhysRevE.107.056601], were actually already acknowledged and discussed in the original publication. Although the observed relationship between the released heat and the spectral entropy of the correlated noise is not universal (but limited to one-parameter Lorentzian spectra), the existence of such a clear relationship is a solid experimental finding. It not only gives a convincing explanation for the surprising thermodynamics observed in the transitions between nonequilibrium steady states, but also provides new tools for the analysis of nontrivial baths. In addition, by using different measures of the correlated noise information content, it may be possible to generalize these results to non-Lorentzian spectra.