  We present exploratory studies of the 3D proton tomography through polarized
$T$-odd gluon TMDs at leading twist, obtained in a spectator-model framework.
We embody in our approach a flexible parameterization for the spectator-mass
spectral function, suited to catch both small- and moderate-$x$ effects. All
these studies are relevant to unveil the gluon dynamics inside hadrons, which
represents a core research line of studies at new-generation colliders, such as
the Electron-Ion Collider, NICA-SPD, the High-Luminosity LHC, and the Forward
Physics Facility.
