Recent observations have revealed remarkable insights into the gas reservoir in the circumgalactic medium (CGM) of galaxy haloes. In this paper, we characterize the gas in the vicinity of Milky Way and Andromeda analogues in the HESTIA (High resolution Environmental Simulations of The Immediate Area) suite of constrained Local Group (LG) simulations. The HESTIA suite comprise of a set of three high-resolution AREPO-based simulations of the LG, run using the Auriga galaxy formation model. For this paper, we focus only on the z = 0 simulation data sets and generate mock skymaps along with a power spectrum analysis to show that the distributions of ions tracing low-temperature gas (H I and Si III) are more clumpy in comparison to warmer gas tracers (O VI, O VII, and O VIII). We compare to the spectroscopic CGM observations of M31 and low-redshift galaxies. HESTIA underproduces the column densities of the M31 observations, but the simulations are consistent with the observations of low-redshift galaxies. A possible explanation for these findings is that the spectroscopic observations of M31 are contaminated by gas residing in the CGM of the Milky Way.