We present TERRA-NG, a portable, GPU-accelerated, matrix-free mantle-convection code. A single Kokkos C++ implementation runs at scale on NVIDIA, AMD, and Intel GPU supercomputers. TERRA-NG has a deliberately narrow design: built on a radially extruded mesh of spherical wedges, tailored to the spherical shell geometry, which enables domain-specific optimizations like single quadrature-point integral-evaluations, radial coordinate storage compression and radial shared-memory tiling. The corresponding low-order <em>W</em><sub>1</sub>-iso-<em>W</em><sub>2</sub>/<em>W</em><sub>1</sub> wedge-based Stokes--energy discretisation is verified against the Zhong et al.(2008) spherical-shell convection benchmark suite. We showcase TERRA-NG through strong- and weak-scaling on the JUWELS Booster (NVIDIA A100), MareNostrum 5 (NVIDIA H100), LUMI-G (AMD MI250X), Hunter (AMD MI300A APU), and SuperMUC-NG Phase 2 (Intel PVC) supercomputers. Coupled mantle convection simulations at ∼11 km and ∼5.6 km radial spacing (∼2.8 B and ∼22 B DoFs) can be run routinely on standard node partitions of all considered systems. Global ∼1 km-per-gridpoint mantle convection (∼1.4 T DoFs) is feasible on an extreme-scale allocation, and a sub-km hero-run at ∼0.7 km grid spacing scaling up to ∼11,000 GPUs of LUMI-G (∼11 T DoFs) shows the potential of the code on future, larger machines.