We present an updated measurement of the diffuse astrophysical neutrino flux using Baikal-GVD cascade data collected between April 2018 to March 2024. In this period, the detector grew from 15% to 55% of its baseline cubic kilometer configuration. The diffuse astrophysical neutrino flux is detected with a statistical significance of 5.1 $\sigma$. Assuming a single power law model of the astrophysical neutrino flux with identical contribution from each neutrino flavor, the following best-fit parameter values are found: the spectral index $\gamma_{astro}$ = 2.64$^{+0.09}_{-0.11}$ and the flux normalization $\phi_{astro}$ = 4.42$^{+2.31}_{-1.29}\times10^{-18} \text{GeV}^{-1}\text{cm}^{-2}\text{s}^{-1}\text{sr}^{-1}$ per one flavor at 100 TeV. These results are broadly consistent with IceCube measurements.