Counting conjecture for surface subgroups in finite-volume hyperbolic manifolds

Let $M=\mathbb H^n/\Gamma$ be a complete hyperbolic $n$-manifold of finite volume. Let $n(g,M)$ and $s(g,M)$ denote the counting functions for the relevant surface subgroups in $M$; the source uses these quantities without further definition.

Counting conjecture. There exists a constant $C(M)$ such that

$$\lim_{g\to\infty}\frac{1}{g}\sqrt[2g]{n(g,M)}=\lim_{g\to\infty}\frac{1}{g}\sqrt[2g]{s(g,M)}=C(M).$$

This conjecture extends the proposed counting asymptotics from closed hyperbolic $3$-manifolds to complete finite-volume hyperbolic manifolds in arbitrary dimension. The surrounding discussion motivates counting conjugacy classes and commensurability classes of surface subgroups, but the supplied text gives no evidence that the conjecture has been resolved.