Stellar obliquity () and orbital eccentricity () trace the dynamical histories of close-in giant planets, but the current observational picture is assembled from heterogeneous analyses that have obscured population-level trends. In this work, we homogeneously refit systems with Rossiter-McLaughlin (RM) measurements by performing a joint global fit to spectral energy distributions, transit light curves, mid-transit times, out-of-transit and in-transit radial velocities, yielding self-consistent posterior distributions for the physical and orbital parameters of both stars and planets across 255 systems. Restricting to 145 single-star systems with reliable planet-mass measurements, we uncover pronounced structure in the plane that depends on planet mass: (i) sub-Saturns () can be both eccentric and misaligned; (ii) Jupiters () are misaligned only on circular orbits; and (iii) super Jupiters and brown dwarfs () are aligned across the full eccentricity range. A two-dimensional Kolmogorov-Smirnov test shows that the joint distributions differ significantly among these three mass regimes. These trends demonstrate that depends jointly on eccentricity and planet mass, implying that obliquity alone is not a unique tracer of evolutionary history and underscoring the need for a unified framework for the origins of spin-orbit misalignment. The full catalog from this work is publicly available at https://www.stellarobliquity.com .

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