Recent observations of the Galactic component of the high-energy neutrino flux, together with the detection of the diffuse Galactic gamma-ray emission up to sub-PeV energies, open new possibilities to study the acceleration and propagation of cosmic rays in the Milky Way. At the same time, both large non-astrophysical backgrounds at TeV energies and scarcity of neutrino events in the sub-PeV band currently limit these analyses. Here we use the sample of cascade events with estimated neutrino energies above 200 TeV, detected by the partially deployed Baikal Gigaton Volume Detector (GVD) in six years of operation, to test the continuation of the Galactic neutrino spectrum to sub-PeV energies. We find that the distribution of the arrival directions of Baikal-GVD cascades above 200 TeV in the sky suggests a strong excess of neutrinos from low Galactic latitudes. We find the excess above 200 TeV also in the most recent IceCube public data sets, both of cascades and tracks. The significant (3.6σ in the combined analysis) flux of Galactic neutrinos above 200 TeV challenges often-used templates for neutrino search based on cosmic-ray simulations.