Various theoretical models predict cosmic neutrinos with multi-PeV energies. The recent detection of a ∼10^17 eV neutrino in the KM3NeT experiment suggests that these energetic particles can be studied with present-day installations. Here, we present upper limits on the flux of astrophysical neutrinos with energies (10^15.5--10^20) eV obtained with the largest liquid-water neutrino telescope, the Baikal Gigaton Volume Detector (GVD), operation using cascade-like events. We discuss astrophysical implications of these results and constrain several cosmogenic neutrino scenarios using a combination of Baikal-GVD, KM3NeT, IceCube, and Auger data.