Optical imaging through scattering media remains a fundamental challenge in modern optics, particularly in reconstructing the full polarization state of structured lights after severe wavefront distortions. Here, we present a computational framework integrating a polarization-multiplexed metasurface and a physics-informed deep neural network. First-time full-Stokes imaging through strong scattering media in a single shot proves that severely damaged high-dimensional light fields can be reconstructed with high accuracy even at optical depths exceeding 11 transport mean free paths. Incorporating Stokes-vector orthogonality constraints as regularization terms in the loss function enables the model to effectively disentangle scattering noise from the polarization information, leading to their improved accuracy and quality. The collaborative design not only underscores its robustness and effectiveness but also enables effective camouflage penetration in complex scenarios where conventional intensity-only imaging fails, offering critical technological potential for addressing key limitations in biomedical diagnostics and autonomous navigation.