  We investigate how the X-ray circumgalactic medium (CGM) of present-day
galaxies depends on galaxy morphology and azimuthal angle using mock
observations generated from the EAGLE cosmological hydrodynamic simulation. By
creating mock stacks of {\it eROSITA}-observed galaxies oriented to be edge-on,
we make several observationally-testable predictions for galaxies in the
stellar mass range $M_\star=10^{10.7-11.2}\;$M$_{\odot}$. The soft X-ray CGM of
disc galaxies is between 60 and 100\% brighter along the semi-major axis
compared to the semi-minor axis, between 10-30 kpc. This azimuthal dependence
is a consequence of the hot ($T>10^6$ K) CGM being non-spherical: specifically
it is flattened along the minor axis such that denser and more luminous gas
resides in the disc plane and co-rotates with the galaxy. Outflows enrich and
heat the CGM preferentially perpendicular to the disc, but we do not find an
observationally-detectable signature along the semi-minor axis. Spheroidal
galaxies have hotter CGMs than disc galaxies related to spheroids residing at
higher halos masses, which may be measurable through hardness ratios spanning
the $0.2-1.5$ keV band. While spheroids appear to have brighter CGMs than discs
for the selected fixed $M_\star$ bin, this owes to spheroids having higher
stellar and halo masses within that $M_\star$ bin, and obscures the fact that
both simulated populations have similar total CGM luminosities at the exact
same $M_\star$. Discs have brighter emission inside 20 kpc and more steeply
declining profiles with radius than spheroids. We predict that the {\it
eROSITA} 4-year all-sky survey should detect many of the signatures we predict
here, although targeted follow-up observations of highly inclined nearby discs
after the survey may be necessary to observe some of our azimuthally-dependent
predictions.
