Predicting battery performance from real electrode and particle microstructures increasingly depends on models that can (i) operate directly on 3D segmented images, (ii) capture coupled multiphysics, including phase transformations in complex morphologies, and (iii) run fast enough to enable parameter calibration and design loops. We present how phase-field methods enable the detailed study of mosaic-like (spatially heterogeneous) phase transformations in high-capacity electrode materials and how, combined with GPU-ready implementations, they pave the way for future microstructure design. By combining the smoothed boundary method with a state-of-the-art multiphase-field formulation (MP-SBM), we simulate the (dis)charge behaviour of polycrystalline, strongly anisotropic, nanoporous agglomerates. We show that phase-field methods provide a powerful bridge across scales thanks to their thermodynamic consistency between Gibbs free energies reconstructed from experimental open-circuit voltage data and energetics from ab initio methods (DFT). Applied to LiNiO2, a high-capacity layered oxide, simulations resolve the sequence of reversible H1-M-H2-H3 transformations and predict a strong morphology dependence of phase-transition pathways: dense agglomerates exhibit a shrinking-core-like progression governed by diffusion limitation, whereas nanoporous architectures promote heterogeneous mosaic patterns on the grain-scale enabled by increased reactive surface access and phase nucleation at high-curvature microstructural features. These mechanistic insights directly inform microstructure design and fast-charging protocols. To translate such models into practical tools that operate directly on microscopy data and support inverse design, we require GPU-ready, differentiable voxel simulations. The Python package evoxels targets large 3D volumes, integrates PyTorch/JAX backends with advanced time-stepping, and supports autodifferentiation. This enables scaling phase-field battery models towards 1000^3 voxel domains and microstructure optimisation directly on 3D reconstructions.