  We do a careful investigation of the prospects of dark energy (DE)
interacting with cold dark matter (CDM) in alleviating the $S_8$ clustering
tension. To this end, we consider various well-known parametrizations of the DE
equation of state (EoS), and consider perturbations in both the dark sectors,
along with an interaction term. Moreover, we perform a separate study for the
phantom and non-phantom regimes. Using CMB, BAO and SNIa datasets, the
constraints on the model parameters for each case have been obtained and a
generic reduction in the $H_0-\sigma_{8,0}$ correlation has been observed, both
for constant and dynamical DE EoS. This reduction, coupled with a significant
negative correlation between the interaction term and $\sigma_{8,0}$,
contributes to easing the clustering tension by lowering $\sigma_{8,0}$ to
somewhere in between the early CMB and late-time clustering measurements for
the phantom regime, for almost all the models under consideration. In addition,
this is achieved without exacerbating the Hubble tension. In this regard, the
CPL and JBP models perform the best in relaxing the $S_8$ tension to
$<1\sigma$. However, for the non-phantom regime the $\sigma_{8,0}$ tension
tends to have worsened, which reassures the merits of phantom dark energy from
latest data. We further do an investigation of the role of RSD datasets and
find an overall reduction in tension, with a value of $\sigma_{8,0}$ relatively
closer to the CMB value. We finally check if further extensions of this
scenario, like the inclusion of the sound speed of dark energy and warm dark
matter interacting with DE, can have some effects.
