  This paper presents a new sample of 19 unique galaxies and galaxy groups at
$z\approx1$ from the CUBS program, which is designated as the CUBSz1 sample. In
this CUBSz1 sample, nine galaxies or galaxy groups show absorption features,
while ten systems do not have detectable absorption with 2-$\sigma$ upper
limits of log$N$(HeI)/cm$^{-2}\lesssim 13.5$ and log$N$(OV)/cm$^{-2}\lesssim
13.3$. Environmental properties of the galaxies, including galaxy
overdensities, the total stellar mass and gravitational potential summed over
all nearby neighbors, and the presence of local ionizing sources, are found to
have a significant impact on the observed CGM absorption properties.
Specifically, massive galaxies and galaxies in overdense regions exhibit a
higher rate of incidence of absorption. At the same time, the observed CGM
absorption properties in galaxy groups appear to be driven by the galaxy
closest to the QSO sightline, rather than by the most massive galaxy or by
mass-weighted properties. We introduce a total projected gravitational
potential $\psi$, defined as $-\psi/G =\sum M_{{\rm halo}}/d_{{\rm proj}}$
summed over all group members, to characterize the overall galaxy environment.
This projected gravitational potential correlates linearly with the maximum
density detected in each sightline, consistent with higher-pressure gas being
confined in deeper gravitational potential wells. In addition, we find that the
radial profile of cool gas density exhibits a general decline from the inner
regions to the outskirts, being in pressure balance with the hot halo. Finally,
we note that the ionizing flux from nearby galaxies can generate an elevated
$N$(HI)/$N$(HeI) ratio, which in turn provides a unique diagnostic of possible
local sources contributing to the ionizing radiation field.
