Euclidean rectifiability of metric spheres in sub-Finsler Carnot groups

Let $\mathbb G$ be a sub-Finsler Carnot group, and let its metric spheres be the level sets of the Carnot–Carathéodory distance associated with a sub-Finsler structure. Euclidean rectifiability conjecture. Metric spheres in sub-Finsler Carnot groups are Euclidean codimension-one rectifiable.

If true in complete generality, this would extend Euclidean rectifiability of sub-Finsler spheres beyond the step-$2$ setting addressed by the paper. The source does not provide a resolution.