  We use multi-object near-infrared (NIR) spectroscopy with VLT/KMOS to
investigate the role of the environment in the evolution of the ionized gas
properties of narrow-band selected H$\alpha$ emitters (HAEs) in the Spiderweb
protocluster at $z=2.16$. Based on rest-frame optical emission lines, H$\alpha$
and [NII]$\lambda$6584, we confirm the cluster membership of 39 of our targets
(i.e. 93% success rate), and measure their star-formation rates (SFR),
gas-phase oxygen abundances and effective radius. We parametrize the
environment where our targets reside by using local and global density
indicators based on previous samples of spectroscopic and narrow-band cluster
members. We find that star-forming galaxies embedded in the Spiderweb
protocluster display SFRs compatible with those of the main sequence and
morphologies comparable to those of late-type galaxies at $z=2.2$ in the field.
We also report a mild gas-phase metallicity enhancement ($0.6\pm0.3$ dex) at
intermediate stellar masses. Furthermore, we identify two UVJ-selected
quiescent galaxies with residual H$\alpha$-based star formation and find signs
of extreme dust obscuration in a small sample of SMGs based on their FIR and
H$\alpha$ emission. Interestingly, the spatial distribution of these objects
differs from the rest of HAEs, avoiding the protocluster core. Finally, we
explore the gas fraction-gas metallicity diagram for 7 galaxies with molecular
gas masses measured by ATCA using CO(1-0). In the context of the gas-regulator
model, our objects are consistent with relatively low mass-loading factors,
suggesting lower outflow activity than field samples at the cosmic noon and
thus, hinting at the onset of environmental effects in this massive
protocluster.
