Safronov's root-of-unity skein conjecture

Let $M$ be a closed 3-manifold, let $q$ be a good root of unity, and let $G^\vee$ be the metaplectic dual group. Let $\mathrm{Loc}_{G^\vee}(M)$ be the character stack of $G^\vee$-local systems on $M$.

Safronov's root-of-unity skein conjecture. There is a line bundle $\mathcal{L}_q$ on $\mathrm{Loc}_{G^\vee}(M)$ such that

$$\mathrm{Sk}_{G,q}(M)\cong \mathrm{H}^0(\mathrm{Loc}_{G^\vee}(M),\mathcal{L}_q).$$

This is a root-of-unity analogue of the generic skein–DT sheaf comparison. The source attributes the conjecture to Pavel Safronov and gives no resolution.