Structured-Light Control of Goniopolar Thermoelectricity in NaSn\texorpdfstring{$_2$}{2}As\texorpdfstring{$_2$}{2}
Goniopolar metals exhibit opposite thermoelectric polarities along different crystallographic directions, enabling zero-field transverse thermoelectricity but offering few means for external control. Here we show that a spatially structured Laguerre--Gaussian vector potential can programmably reconstruct the goniopolar phase space of NaSn$_2$As$_2$. First-principles-derived Wannier transport with bond-dependent Peierls coupling reveals two OAM-dependent spatial scaling laws: the radial response follows the Laguerre--Gaussian radius $r_{\max}\propto\sqrt{|\ell|}$, while calculations for $|\ell|=2$--5 yield a dominant angular harmonic $m_{\mathrm{dom}}=2|\ell|$, encoding the optical winding in a frequency-doubled thermoelectric response. Increasing $|\ell|$ simultaneously reconstructs pre-existing goniopolar windows, enhancing a representative window by approximately 17\% at $|\ell|=5$. By contrast, reversing $\ell$ at fixed polarization produces only a small correction that approximately interchanges upon polarization reversal. Energy-resolved transport reveals that the structured field redistributes in-plane and cross-plane electronic velocities, shifting the directional Seebeck-zero boundaries that define the goniopolar state. These results establish vortex position and OAM magnitude as programmable control coordinates for goniopolar thermoelectricity.