The neutral silicon–vacancy (SiV${}^0$) center in diamond combines inversion symmetry with optical emission, making it a robust quantum emitter resilient to stray electric fields. Using first-principles density-functional theory, we quantify its response to isotropic strain spanning strong compression and tensile regimes (effective hydrostatic pressures of approximately $-80$ to $180$~GPa). The coexistence of doubly degenerate $e_g$ and $e_u$ levels produces a structural instability captured by a quadratic product Jahn–Teller model. Under isotropic compression, the zero-phonon line blue-shifts nearly linearly while the $E_g$ phonon stiffens, suppressing vibronic instabilities and reducing Jahn–Teller quenching. Consequently, the Ham-reduced excited-state spin–orbit splitting increases substantially and the dark–bright vibronic gap widens. In contrast, isotropic tensile strain enhances vibronic effects and induces symmetry breaking beyond a critical strain, with tunneling-mediated dynamical averaging at the onset. Throughout the symmetry-preserving regime, parity remains well defined, so isotropic strain alone does not activate the dark transition. Charge-transition levels indicate photostability of the emission deep into the compressive regime, and near the highest photostable deformation ($\sim 100$~GPa), the radiative lifetime increases due to a reduced transition dipole moment despite the increasing optical energy. These trends yield compact calibration relations linking optical and spin observables to isotropic strain and establish SiV${}^0$ as a symmetry-protected, strain-tunable quantum emitter operating into the multi-megabar-equivalent regime.