The interplay between AGN photo-ionization, radio jet, and star formation in the z $\sim$ 3.5 radio galaxy 4C +03.24
High-redshift radio galaxies (HzRGs) are among the most powerful radio sources, and are associated with the most massive galaxies and dense environments at redshifts z $\gtrsim$ 1. They are ideal laboratories for studying how Active Galactic Nuclei (AGN) events can shape the evolution of galaxies, as intense radiation, jets, and star formation are simultaneously observed. We present JWST/NIRSpec integral-field spectroscopy ($\sim$ 1.6 kpc spatial resolution) of the 4C +03.24 system, a powerful HzRG at z $\sim$ 3.5 with a bolometric luminosity of $\sim 10^{47.6}$ erg s$^{-1}$. We identify kinematically disturbed regions in the warm ($\sim 10^4$ K) ionized gas by decomposing the emission-line spectra into multiple Gaussian components, which is crucial to avoid overestimating the outflow properties. The outflow power peaks at $\sim$ 2 kpc away from the nucleus, with a corresponding low kinetic coupling efficiency of $\sim 8_{-5}^{+7} \times 10^{-3}$ %. A combined analysis of the rest-frame optical and UV (from VLT/MUSE and HST imaging) continua reveals an extended emission (spanning $\sim$ 14 kpc), which we interpret as partially tracing star-forming regions. With a clearly delineated bipolar morphology, we show that the AGN photo-ionization dominates the ionization of the interstellar medium (ISM) along the radio jet axis. The [C II]$λ$158$μ$m emission gap in this region might be direct evidence of negative AGN feedback. We also discuss a possible scenario where 4C +03.24 could be situated in an overdense environment experiencing multiple galaxy interactions, and the possibility of jet-induced star-formation.