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 detected 24 rest-frame optical emission lines from the z = 3.5892 radio galaxy 4C+19.71, which 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_⋆ ∼ 10¹¹ M_⊙ 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. Subkiloparsec resolution reveals filamentary structures and emission blobs in the warm ionized ISM distributed on scales of ∼5 to ∼20 kpc. A large fraction of the extended gaseous nebula is located near the systemic velocity. This nebula thus may be the patchy ISM that is illuminated by the AGN after the passage of the jet. A radiative-driven outflow was observed within ∼5 kpc from the nucleus. The inefficient coupling (≲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.