1-affineness conjecture for the de Rham local systems prestack

Let $G$ be an affine algebraic group, and let $\operatorname{LocSys}_G(\overset{\circ}{{\mathcal D}})$ denote the prestack of de Rham $G$-local systems on the punctured formal disc $\overset{\circ}{{\mathcal D}}$. 1-affineness conjecture. The prestack $\operatorname{LocSys}_G(\overset{\circ}{{\mathcal D}})$ is 1-affine for any affine algebraic group $G$. This claim concerns the 1-affineness of a central prestack in local geometric Langlands; the supplied text does not establish whether it is intended as a conjecture or whether it has been resolved.