Recent PTA analyses reporting evidence for a nanohertz common-spectrum process motivate targeted tests of whether any anisotropic component of the stochastic gravitational-wave background (SGWB) is correlated with the nearby large-scale structure (LSS), as anticipated for an astrophysical background dominated by supermassive black hole binaries. We present the first Bayesian PTA likelihood analysis that embeds an externally observed, full-sky galaxy-survey LSS template directly as an overlap-reduction-function (ORF) component. Using the 2MASS photometric redshift (2MPZ) galaxy catalog, we construct low-multipole LSS-correlated ORF templates in two redshift slices (0 < z ⩽ 0.1 and 0.1 < z ⩽ 0.2) and model PTA cross-correlations as \(\Gamma_{ab}=\Gamma_{ab}^{\text{HD}}+\Sigma_{i}\epsilon_{i}\Gamma_{ab}^{\text{LSS}(i)}\) , where ϵi quantifies the amplitude of an SGWB component whose angular correlations project onto the fixed 2MPZ LSS templates. Applying this framework to the NANOGrav 15-year dataset, we find no evidence for an LSS-correlated component: the inferred ϵi values are consistent with zero in both single-bin and two-bin analyses (e.g., \(\epsilon_{1}=0.20_{-1.66}^{+1.68}\) and \(\epsilon_{2}=-0.11_{-1.83}^{+2.04}\) ; 68% credible intervals), and Bayes factors favor the isotropic Hellings-Downs hypothesis ( \({\cal{B}}_{\text{HD+LSS}_{1},\text{HD}}=0.40,\ {\cal{B}}_{\text{HD+LSS}_{2},\text{HD}}=0.43,\ {\cal{B}}_{\text{HD+LSS}_{1+2},\text{HD}}=0.11 \) ). We therefore place upper limits on any 2MPZ-traced, LSS-correlated contribution to the SGWB at z < 0.2. More broadly, our framework provides a reproducible pathway for incorporating observed LSS information into PTA anisotropy searches and naturally motivates extensions to finer redshift tomography and next-generation PTA datasets.
