High‑order spectral‑element methods are widely used in the numerical simulation of incompressible flows, owing to their favorable accuracy properties, arithmetic intensity, and scalability on modern high‑performance computing architectures. Their extension to fully compressible flows, however, remains challenging due to the presence of shocks and under‑resolved discontinuities, as well as the difficulty of designing stable, performance‑portable implementations on heterogeneous CPU-GPU platforms. In particular, existing GPU‑accelerated spectral‑element solvers are largely restricted to incompressible or low‑Mach formulations, whereas fully compressible GPU solvers typically rely on discontinuous Galerkin or flux‑reconstruction discretisations rather than continuous spectral elements. In this work, we introduce a fully compressible Navier–Stokes solver implemented in the open‑source CFD framework Neko, based on a continuous spectral‑element discretisation and stabilised using an entropy‑viscosity regularisation. The entropy‑viscosity mechanism acts as a vanishing‑viscosity regularisation that is active only in non‑smooth regimes, while preserving high‑order accuracy for smooth solutions and maintaining a compact, element‑local operator structure. The solver is designed with performance portability as a primary objective and supports execution on CPUs as well as AMD and NVIDIA GPUs through a unified backend abstraction. We assess the numerical properties of the method using a collection of canonical compressible test problems, including shock‑dominated configurations and under‑resolved turbulent flows. Performance results demonstrate efficient utilisation of contemporary heterogeneous architectures, with scaling behaviour comparable to that of established incompressible spectral‑element solvers. The proposed solver extends the applicability of spectral‑element methods to fully compressible flow simulations on modern HPC systems and provides a foundation for future developments in high‑order, performance‑portable compressible CFD.