  We study the landscape of lower-dimensional vacua of the SM coupled to
gravity in the presence of the ``dark dimension'' of size $R_\perp$ in the
micron range, focusing on the validity of the swampland conjecture forbidding
the presence of non-SUSY AdS vacua in a consistent quantum gravity theory. We
first adopt the working assumption that right-handed neutrinos propagate in the
bulk, so that neutrino Yukawa couplings become tiny due to a volume
suppression, leading to naturally light Dirac neutrinos. We show that the
neutrino KK towers compensate for the graviton tower to maintain stable dS
vacua found in the past, but neutrino oscillation data set restrictive bounds
on $R_\perp$ and therefore the first KK neutrino mode is too heavy to alter the
shape of the radon potential or the required maximum mass for the lightest
neutrino to carry dS rather than AdS vacua found in the absence of the dark
dimension, $m_{1,{\rm max}}\lesssim 7.63~{\rm meV}$. We also show that a very
light gravitino (with mass in the meV range) could help relax the neutrino mass
constraint $m_{1,{\rm max}} \lesssim 50~{\rm meV}$. The differences for the
predicted total neutrino mass $\sum m_\nu$ among these two scenarios are within
reach of next-generation cosmological probes that may measure the total
neutrino mass with an uncertainty $\sigma (\sum m_\nu) = 0.014~{\rm eV}$. We
also demonstrate that the KK tower of a very light gravitino can compensate for
the graviton tower to sustain stable dS vacua and thus right-handed neutrinos
can (in principle) be locked on the brane. For this scenario, Majorana
neutrinos could develop dS vacua, which is not possible in the SM coupled to
gravity. Finally, we investigate the effects of bulk neutrino masses in
suppressing oscillations of the 0-modes into the first KK modes to relax the
oscillation bound on $R_\perp$.
