  The paper presents the analysis of optically selected GAMA groups and
clusters in the SRG/eROSITA X-ray map of eFEDS (eROSITA Final Equatorial Depth
Survey), in the halo mass range $10^{13}-5{\times}10^{14}$ $M_{\odot}$ and at
$z < 0.2$. All X-ray detections have a clear GAMA counterpart, but most of the
GAMA groups in the halo mass range $10^{13}-10^{14}$ $M_{\odot}$ remain
undetected. We compare the X-ray surface brightness profiles of the eROSITA
detected groups with the mean stacked profile of the undetected low-mass halos
at fixed halo mass. Overall, we find that the undetected groups exhibit less
concentrated X-ray surface brightness, dark matter, and galaxy distributions
with respect to the X-ray detected halos. The mean gas mass fraction profiles
are consistent in the two samples within 1.5$\sigma$, indicating that the gas
follows the dark matter profile. The low mass concentration and the magnitude
gap indicate that these systems are young. They reside with a higher
probability in filaments while X-ray detected groups favor the nodes of the
Cosmic Web. Because of the lower central emission, the undetected systems tend
to be X-ray under-luminous at fixed halo mass and to lie below the
$L_X-M_{halo}$ relation. Interestingly, the X-ray detected systems inhabiting
the nodes scatter the less around the relation, while those in filaments tend
to lie below it. We do not observe any strong relationship between the system
X-ray appearance and the AGN activity. We cannot exclude the role of the past
AGN feedback in affecting the gas distribution over the halo lifetime. However,
the data suggests that the observed differences might be related to the halo
assembly bias.

Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies;High Energy Astrophysical Phenomena