  A major challenge for magnetic skyrmions in atomically thin van der Waals
(vdW) materials is reliable skyrmion detection. Here, based on rigorous
first-principles calculations, we show that all-electrical skyrmion detection
is feasible in 2D vdW magnets via scanning tunneling microscopy (STM) and in
planar tunnel junctions. We use the nonequilibrium Green's function method for
quantum transport in planar junctions, including self-energy due to electrodes
and working conditions, going beyond the standard Tersoff-Hamann approximation.
We obtain a very large tunneling anisotropic magnetoresistance (TAMR) around
the Fermi energy for a vdW tunnel junction based on
graphite/Fe$_3$GeTe$_2$/germanene/graphite. For atomic-scale skyrmions the
noncollinear magnetoresistance (NCMR) reaches giant values. We trace the origin
of the NCMR to spin-mixing between spin-up and -down states of $p_z$ and
$d_{z^2}$ character at the surface atoms. Both TAMR and NCMR are drastically
enhanced in tunnel junctions with respect to STM geometry due to orbital
symmetry matching at the interface.
