The phase-field method provides a variational framework for modeling brittle fracture by regularizing sharp crack discontinuities and enabling crack propagation. In its classical variational interpretation, the phase-field formulation represents a regularized approximation of brittle fracture that is expected to converge to linear elastic fracture mechanics (LEFM) as the regularization length-scale parameter tends to zero. Previous numerical convergence studies have largely been restricted to one-dimensional or highly simplified configurations, where limited Γ-convergence results were obtained under specific ratios of regularization length to mesh size, often without a clear mechanistic interpretation of these optimal parameter choices. More recent two-dimensional investigations have examined convergence of critical energy release rates and optimal crack growth for decreasing length scales, while also motivating a physical interpretation of the length-scale parameter for modeling strength-dominated fracture processes. While effective for specific modeling objectives, such approaches depart from the classical variational structure and do not primarily aim to recover LEFM in the vanishing length-scale limit. In this work, we present a numerical convergence study of the classical AT2 phase-field fracture model in two- and three-dimensional specimens containing large pre-existing cracks. Coordinated refinement of the regularization length and mesh size is performed, and convergence is assessed with respect to the fracture energy Γ, the critical energy release rate Gc evaluated using contour integrals, and local crack path evolution under quasi-static loading. Results are compared against established LEFM benchmark solutions. The results indicate that recovery of LEFM behavior with the AT2 formulation requires strict coupling between mesh resolution and regularization length, ensuring resolution of the diffusive crack zone and its associated energy dissipation. Optimal regularization-to-mesh ratios observed in lower-dimensional studies are interpreted as a balance between under-resolution of the phase-field crack profile and excessive artificial fracture energy dissipation. In two- and three-dimensional settings, this balance becomes geometry- and loading-dependent, leading to distinct convergence rates. Finite regularization lengthscales result in persistent deviations in energy release rates and crack paths, even under mesh refinement.