  We compute the differential yield for quark anti-quark dijet production in
high-energy electron-proton and electron-nucleus collisions at small $x$ as a
function of the relative momentum $\boldsymbol{P}_\perp$ and momentum imbalance
$\boldsymbol{k}_\perp$ of the dijet system for different photon virtualities
$Q^2$, and study the elliptic and quadrangular anisotropies in the relative
angle between $\boldsymbol{P}_\perp$ and $\boldsymbol{k}_\perp$. We review and
extend the analysis in [1], which compared the results of the Color Glass
Condensate (CGC) with those obtained using the transverse momentum dependent
(TMD) framework. In particular, we include in our comparison the improved TMD
(ITMD) framework, which resums kinematic power corrections of the ratio
$k_\perp$ over the hard scale $Q_\perp$. By comparing ITMD and CGC results we
are able to isolate genuine higher saturation contributions in the ratio
$Q_s/Q_\perp$ which are resummed only in the CGC. These saturation
contributions are in addition to those in the Weizs\"ackerWilliams gluon TMD
that appear in powers of $Q_s/k_\perp$. We provide numerical estimates of these
contributions for inclusive dijet production at the future Electron-Ion
Collider, and identify kinematic windows where they can become relevant in the
measurement of dijet and dihadron azimuthal correlations. We argue that such
measurements will allow the detailed experimental study of both kinematic power
corrections and genuine gluon saturation effects.
