Nanoscale origin of thermal anisotropy in monoclinic \texorpdfstring{$β$-Ga$_2$O$_3$}{beta-Ga2O3}
Monoclinic $β$-Ga$_2$O$_3$ is a promising ultra-wide-bandgap semiconductor for power electronics, but its low and anisotropic thermal conductivity limits heat removal, making it a compelling model system for nanoscale thermal transport studies. Here, we demonstrate a pronounced nanoscale enhancement of thermal anisotropy and uncover the underlying phonon mechanism by combining complementary thermal and acoustic spectroscopy techniques with first-principles calculations. Anisotropic thermoreflectance thermometry determines the full thermal-conductivity tensor from angular measurements within the (100), (010), and (001) crystallographic planes. Angle-resolved Brillouin light scattering reveals that low-frequency acoustic phonons exhibit only weak velocity anisotropy, insufficient to account for the measured thermal anisotropy. Frequency-resolved ab initio Green--Kubo calculations show that the bulk anisotropy pattern emerges only when the accumulated conductivity includes phonon modes above 4 THz, whereas the sub 3 THz acoustic contributions are nearly isotropic. Extreme-ultraviolet transient thermal grating spectroscopy reveals that reducing the grating period to 28 nm strongly enhances the in-plane thermal anisotropy, most markedly in the (001) plane, where it reaches nearly twice its macroscopic value. Reconstructed and calculated mean-free-path (MFP) accumulation functions link this enhancement to the stronger directional contrast of short-MFP phonons. Together, these results identify high-frequency, short-MFP phonons as the dominant origin of thermal anisotropy in $β$-Ga$_2$O$_3$, while low-frequency phonons attenuate the directional contrast at macroscopic scales.