This paper presents a unified and computationally efficient framework for modeling antennas embedded in spherically stratified media, applicable to implantable biomedical antennas and radome-enclosed systems. The method separates the characterization of the radiator from that of the surrounding medium by combining the antenna's free-space generalized scattering matrix (GSM) with a set of extended spherical scattering operators (SSOs). This decoupling enables rapid reevaluation under arbitrary changes of the spherical medium without re-simulating the antenna, yielding orders-of-magnitude speedups over traditional DGF-based MoM approaches. The SSO formulation accommodates multilayer, radially inhomogeneous, and radially uniaxial anisotropic profiles, and the GSM can be obtained from diverse numerical solvers or far-field data, supporting array-level synthesis and measurement-driven modeling. Extensive examples confirm excellent agreement with full-wave and DGF-based solutions, demonstrating the accuracy, generality, and practical versatility of the proposed framework.