Standard Koszulity conjecture for geometric category O

Let $\mathcal{O}_{\!\operatorname{g}}$ be the geometric category $\mathcal{O}$ associated with a conical symplectic resolution and a Hamiltonian torus action. Standard Koszulity conjecture. For any choice of quantization, the category $\mathcal{O}_{\!\operatorname{g}}$ is standard Koszul. This would follow from the corresponding conjecture for algebraic category $\mathcal{O}$ and remains open in general.