Mass--size evolution and the emerging passive--density relation revealed by JWST/NIRCam in the Spiderweb protocluster

We investigate how the environment affects galaxy structure in the Spiderweb protocluster at $z=2.16$ using JWST/NIRCam F115W, F182M, and F410M imaging (rest-frame $\sim 3500${\AA} to $1.4\,\mu$m). We perform homogeneous multi-wavelength parametric modelling of the single-S\'ersic and bulge--disc decomposition for the Spiderweb member sample of 103 galaxies within the JWST field of view (up to $\sim 2\times R_{200}$). Star-forming galaxies follow a mass--size relation broadly consistent with the field, with a mildly steeper trend at the high-mass end within uncertainties. Passive galaxies exhibit a flatter mass--size relation, and their typical size (intercept at fixed stellar mass) lies between that of the coeval field and cluster passive populations, indicating an intermediate evolutionary stage. In both star-forming and passive systems, bulges are systematically more compact than discs. Galaxy sizes decrease slightly with increasing wavelength, whereas ALMA-detected dusty star-forming galaxies exhibit a much steeper wavelength dependence, consistent with centrally concentrated, obscured star formation. The passive fraction depends primarily on local density: it resembles the field at $\Sigma \lesssim 100$--$200\,{\rm gal\,Mpc^{-2}}$ and rises to $\sim60\%$ at $\Sigma \gtrsim 1000\,{\rm gal\,Mpc^{-2}}$, although with relatively large uncertainties due to the small number of galaxies in the highest-density bins, with no significant additional dependence on clustercentric distance. We also find a weak but significant correlation between local density and S\'ersic index (strongest in F410M), but no clear correlation with effective radius or the star-formation rate surface density $\Sigma_{\rm SFR}$. These results support a picture in which quenching and structural transformation are already advanced, while the size growth is still ongoing.