  We present the first results from a JWST program studying the role played by
powerful radio jets in the evolution of the most massive galaxies at the onset
of Cosmic Noon. Using NIRSpec integral field spectroscopy, we detect 24
rest-frame optical emission lines from the $z=3.5892$ radio galaxy 4C+19.71.
4C+19.71 contains one of the most energetic radio jets known, making it perfect
for testing radio-mode feedback on the interstellar medium (ISM) of a
$M_{\star}\sim10^{11}\,\rm M_{\odot}$ galaxy. The rich spectrum enables line
ratio diagnostics showing that the radiation from the active galactic nucleus
(AGN) dominates the ionization of the entire ISM out to at least $25\,$kpc, the
edge of the detection. Sub-kpc resolution reveals filamentary structures and
emission blobs in the warm ionized ISM distributed on scales of $\sim5$ to
$\sim20\,$kpc. A large fraction of the extended gaseous nebula is located near
the systemic velocity. This nebula may thus be the patchy ISM which is
illuminated by the AGN after the passage of the jet. A radiatively-driven
outflow is observed within $\sim5\,$kpc from the nucleus. The inefficient
coupling ($\lesssim 10^{-4}$) between this outflow and the quasar and the lack
of extreme gas motions on galactic scales are inconsistent with other high-$z$
powerful quasars. Combining our data with ground-based studies, we conclude
that only a minor fraction of the feedback processes is happening on $<25\,$kpc
scales.
