  New optical sensors with a segmented photosensitive area are being developed
for the next generation of neutrino telescopes at the South Pole. In addition
to increasing sensitivity to high-energy astrophysical neutrinos, we show that
this will also lead to a significant improvement in sensitivity to MeV
neutrinos, such as those produced in core-collapse supernovae (CCSN). These
low-energy neutrinos can provide a detailed picture of the events after stellar
core collapse, testing our understanding of these violent explosions. We
present studies on the event-based detection of MeV neutrinos with a segmented
sensor and, for the first time, the potential of a corresponding detector in
the deep ice at the South Pole for the detection of extra-galactic CCSN. We
find that exploiting temporal coincidences between signals in different
photocathode segments, a $27\ \mathrm{M}_{\odot}$ progenitor mass CCSN can be
detected up to a distance of 269 kpc with a false detection rate of $0.01$
year$^{-1}$ with a detector consisting of 10000 sensors. Increasing the number
of sensors to 20000 and reducing the optical background by a factor of 140
expands the range such that a CCSN detection rate of $0.08$ per year is
achieved, while keeping the false detection rate at $0.01$ year$^{-1}$.
