Geometric Manin conjecture on the nef section cone

Let $\pi:\mathcal{X}\to B$ be a good Fano fibration. An intersection profile $\lambda$ specifies one generically smooth, geometrically integral irreducible component in each fiber, and $\mathsf{S}_{\lambda}$ is the convex hull of nef integral curve classes having that profile. Let $\mathcal{X}_{\eta}$ be the generic fiber. Geometric Manin conjecture on the nef section cone. For every intersection profile $\lambda$, $\mathsf{S}_{\lambda}$ is a rational polyhedral convex set whose recession cone is $\operatorname{Nef}_{1}(\mathcal{X}_{\eta})$. In characteristic zero this is attributed to LRT23, Corollary 5.8; the source does not state a positive-characteristic resolution.