The Structural Anatomy of Galaxies: Environmental Dependence of Morphological and Quenching Evolution at 0.1 < z < 0.5

We investigate how cluster environments affect galaxy star formation, structure, and stellar populations using spectroscopically-confirmed galaxies in X-ray-selected eROSITA clusters, that have deep HSC-SSP imaging and DESI DR1 spectroscopy. At 0.1<z<0.5, we compare dust-corrected Ha star formation rates (SFRs), effective radii (Re), bulge-to-total light ratios (B/T), and Dn4000 between cluster satellites and a stellar-mass- and redshift-matched field control sample. We identify UVJ-quiescent galaxies and divide the UVJ star-forming population at log(sSFR Ha)= -10.5 yr-1 into actively star-forming and Ha-low systems, the latter referred to as green-valley (GV) galaxies. Cluster--field differences depend strongly on stellar mass, projected cluster-centric radius, and galaxy population. Cluster star-forming galaxies show modest SFR suppression but weak structural offsets. The strongest coupled signatures occur among Ha-low UVJ-star-forming galaxies, particularly low-mass satellites at R<0.5R500, which have lower SFRs, smaller light-weighted sizes, larger B/T, and larger Dn4000 than matched field counterparts. Quiescent galaxies show weaker structural offsets but retain a positive Dn4000 residual. We quantify the joint signal using a Mahalanobis distance based on matched residuals in SFR, Re, B/T, and Dn4000 with a field--field reference covariance. The multivariate offset is largest for low-mass GV galaxies and decreases toward larger projected radius. The broader radial extent of SFR suppression relative to structural offsets suggests that star-formation suppression has a broader environmental reach than structural transformation. These results show that environmental quenching and structural transformation are most strongly coupled in the Ha-low transition population.