Dynamical Architectures of S-type Transiting Planets in Binaries II: A Dichotomy in Orbital Alignment of Small Planets in Close Binary Systems

Stellar multiplicity plays a crucial role in shaping planet formation and dynamical evolution. We present a survey of 54 TESS Objects of Interest (TOIs) within 300 pc that exhibit significant Hipparcos-Gaia astrometric accelerations. We identified 35 TOIs with stellar companions at projected separations between $0.1^{\prime\prime}$ to $2^{\prime\prime}$ (or $10-200$ AU). We also identified 12 TOIs that could host planetary-mass or brown dwarf companions, including 6 that are newly discovered. Furthermore, we perform three-dimensional orbital characterization for 12 binaries hosting confirmed planets or planet candidates, allowing us to constrain the line-of-sight mutual inclination, $\Delta I_{\mathrm{los}}$, between the planetary and binary orbits. Combining our sample with previous measurements, we apply Bayesian hierarchical analysis to a total of 26 binary systems with S-type transiting planets ($r_p<5R_{\oplus}$). Specifically, we fit the $\Delta I_{\mathrm{los}}$ distribution with both single (Rayleigh) and mixture models (two-component Rayleigh and Rayleigh-isotropic mixture). We find the mixture models are strongly favored ($\log Z\gtrsim13.9$, or $\approx$5$\sigma$), indicating the observed planet-binary $\Delta I_{\mathrm{los}}$ values likely originate from two underlying populations: one nearly aligned ($\sigma_1 = 2^{\circ}.4^{+0.7}_{-0.9}$) and one with more scattered mutual inclinations ($\sigma_2 = 23^{\circ}.6^{+8.8}_{-7.1}$). Alternatively, the misaligned systems can be equally well described by an isotropic distribution of inclinations. This observed dichotomy likely reflects different dynamical histories. Notably, the misaligned population only emerges in systems with stellar periastron distances $>40$ AU while systems with close-in or eccentric stellar companions (periastron distances $<40$ AU) preserve planet-binary alignment.