High-fidelity simulations are a key tool to improve the aerodynamic design of aircraft, but the required target accuracy often demands very fine meshes, especially for high-Reynolds-number configurations. Nonconforming hierarchical mesh refinement based on cell subdivision is a powerful means to reduce this cost, as it refines only where the solution requires it and works natively with the linear hybrid meshes commonly used in industry. To be maximally efficient, it should start from an extremely coarse initial mesh. However, when linear meshes are refined, the curved surface of the design is lost, so the mesh has to be kept faithful to the original CAD geometry. To this end, a CAD-driven mesh adaptation workflow is proposed: The next-generation, highly parallel CFD solver computes the flow field, and cells are refined locally, driven by the solution. Inside the boundary layer, refinement is performed on entire cell stacks, preserving the anisotropic layering and keeping the subsequent volume mesh deformation well-posed. The solution and the mesh-to-CAD mapping are transferred from the previous mesh efficiently, exploiting the hierarchical nature of the refinement. New surface node positions are computed on the CAD geometry by a cell-stack-dependent directional projection and supplied to a multi-step volume mesh deformation, which propagates them into the mesh interior while preserving the nonconformity. All steps are performed in memory inside the FlowSimulator framework, enabling their use in high-performance computing environments. The workflow is demonstrated for the transonic ONERA M6 wing test case, starting from an extremely coarse initial mesh of only 2112 cells. Without geometry integration, the refinement converges to a solution that is inconsistent with the actual design, whereas the proposed workflow yields geometry-consistent aerodynamic results. Compared to global refinement, for a given accuracy, the adaptive approach currently offers only a modest gain in cell count, since the stack refinement introduces a significant overhead, which future work aims to reduce.