While Quantum Electrodynamics (QED) and General Relativity independently describe the vacuum's non-linear response to electromagnetic and gravitational fields, their coupled macroscopic behavior requires a unified description. Building upon the Tensorial Dynamical Vacuum (TDV) framework, we propose an integrated Effective Field Theory (EFT) to model these gravito-electromagnetic responses. By formulating the effective vacuum susceptibility as a rank-4 universal response tensor, we demonstrate that the classical Born-Infeld invariants emerge in the geometric limit. In strong-field astrophysical environments such as magnetars, the transverse geometric projection of these coexisting fields along photon geodesics dynamically breaks the $SO(2)$ uniaxial symmetry of pure QED. This superposition transitions the local vacuum condensate into an effectively biaxial optical regime, generating specific geometric signatures: anomalous circular polarization (Stokes $V$) and an asymmetric phase distortion in the linear polarization angle (PA). To reconcile these effects with established terrestrial and cosmological bounds, we propose that the macroscopic dynamical rigidity of the vacuum is locally relaxed via a tachyonic instability, triggered by the direct coupling of the condensate to the electromagnetic invariant near the Schwinger limit. While Stokes $V$ remains inaccessible to current photoelectric detectors, the emergent energy-dependent PA distortion provides a falsifiable phenomenological target for broadband X-ray polarimetry missions such as eXTP.