  Analytical models of galaxy-halo connection such as the Halo Occupation
Distribution (HOD) model have been widely used over the past decades as a means
to intensively test perturbative models on quasi-linear scales. However, these
models fail to reproduce the galaxy-galaxy lensing signal on non-linear scales,
over-predicting the observed signal up to 40%. With ongoing Stage-IV galaxy
surveys such as DESI and EUCLID, it is now crucial to accurately model the
galaxy-halo connection up to intra-halo scales to accurately estimate
theoretical uncertainties of perturbative models. This paper compares the
standard HOD model to an extended HOD framework that incorporates as additional
features galaxy assembly bias and local environmental dependencies on halo
occupation. These models have been calibrated against the observed clustering
and galaxy-galaxy lensing signal of eBOSS Luminous Red Galaxies (LRG) and
Emission Lines Galaxies (ELG) in the range 0.6 < z < 1.1. A combined
clustering-lensing cosmological analysis is then performed on the simulated
galaxy samples of both standard and extended HOD frameworks to quantify the
systematic budget of perturbative models. The extended HOD model offers a more
comprehensive understanding of the connection between galaxies and their
surroundings. In particular, we found that the LRGs preferentially occupy
denser and more anisotropic environments. Our results highlight the importance
of considering environmental factors in galaxy formation models, with an
extended HOD framework that reproduces the observed signal within 20% on scales
below 10 Mpc/h. Our cosmological analysis reveals that our perturbative model
yields similar constraints regardless of the galaxy population, with a better
goodness of fit for the extended HOD. These results suggest that the extended
HOD framework should be used to quantify modeling systematics.
