Galaxy Underdensities Host the Clearest IGM Ly$\alpha$ Transmission and Indicate Anisotropic Reionization

How galaxies drive reionization and what governs its geometry remain fundamental questions. We present JWST/NIRCam wide-field slitless spectroscopy (WFSS) observations toward two of the most Ly$\alpha$-transmissive QSO sightlines near the end of reionization. We find that regions at $z \sim 5.7$ along both sightlines previously found to be low-density in Ly$\alpha$ emitters are also underdense in [O III] emitters, with densities less than half the cosmic mean. Other transmissive regions, however, are found to coincide with average-density environments, indicating that multiple pathways may produce high IGM transmission. For the first time, we measure the two-dimensional cross-correlation between IGM transmission and galaxy positions, revealing evidence for anisotropic ionization geometry. Specifically, we detect enhanced transmission at transverse distances of $\Delta r \sim 0.8$ times the mean free path, consistent with ionizing photons escaping preferentially along large-scale structures that are aligned with, but offset from, the line of sight. This anisotropic escape may contribute to the observed patchiness of reionization and challenges the assumption of isotropic ionized bubble growth in current models.