  Diffuse neutrinos from past supernovae in the Universe present us with a
unique opportunity to test dark matter (DM) interactions. These neutrinos can
scatter and boost the DM particles in the Milky Way halo to relativistic
energies allowing us to detect them in terrestrial laboratories. Focusing on
generic models of DM-neutrino and electron interactions, mediated by a vector
or a scalar boson, we implement energy-dependent scattering cross-sections and
perform detailed numerical analysis of DM attenuation due to electron
scattering in-medium while propagating towards terrestrial experiments. We set
new limits on DM-neutrino and electron interactions for DM with masses in the
range $\sim (0.1, 10^4)~$MeV, using recent data from XENONnT, LUX-ZEPLIN, and
PandaX-4T direct detection experiments. We demonstrate that consideration of
energy-dependent cross-sections for DM interactions can significantly affect
constraints previously derived under the assumption of constant cross-sections,
modifying them by multiple orders of magnitude.
