  Upcoming advances in galaxy surveys and cosmic microwave background data will
enable measurements of the anisotropic distribution of diffuse gas in filaments
and superclusters at redshift $z=1$ and beyond, observed through the thermal
Sunyaev-Zel'dovich (tSZ) effect. These measurements will help distinguish
between different astrophysical feedback models, account for baryons that
appear to be 'missing' from the cosmic census, and present opportunities for
using locally-anisotropic tSZ statistics as cosmological probes. This study
seeks to guide such future measurements by analysing whether diffuse
intergalactic gas is a major contributor to anisotropic tSZ signal in The Three
Hundred Gizmo-Simba hydrodynamic simulations. We apply multiple different halo
boundary and temperature criteria to divide concentrated from diffuse gas at
$z=1$, then create mock Compton-$y$ maps for the separated components. The maps
from 98 simulation snapshots are centred on massive galaxy clusters, oriented
by the most prominent galaxy filament axis, and stacked. Results vary
significantly depending on the definition used for diffuse gas, indicating that
assumptions should be clearly defined when claiming observations of the
warm-hot intergalactic medium. In all cases, the diffuse gas is important,
contributing 25-60% of the tSZ signal in the far field ($>4 h^{-1}$ comoving
Mpc) from the stacked clusters. The gas 1-2 virial radii from halo centres is
especially key. Oriented stacking and environmental selections help to amplify
the signal from the warm-hot intergalactic medium, which is aligned but less
concentrated along the filament axis than the hot halo gas.
