Ben-Zvi–Nadler's Betti geometric Langlands conjecture for nodal curves

Let $\Sigma$ be a compact Riemann surface, let $G$ be a reductive group, and let $\check{G}$ be its Langlands dual group. Write $\operatorname{Bun}_G(\Sigma)$ for the moduli stack of principal $G$-bundles on $\Sigma$, and let $\operatorname{Locsys}_{\check{G}}(\Sigma)$ be the derived moduli stack of Betti $\check{G}$-local systems on $\Sigma$. Denote by $\mathcal{N}$ and $\check{\mathcal{N}}$ the nilpotent singular-support conditions on the two sides. Ben-Zvi–Nadler's Betti geometric Langlands conjecture. There is an equivalence of dg-categories

$$\operatorname{Sh}_{\mathcal{N}}(\operatorname{Bun}_G(\Sigma))\simeq \operatorname{IndCoh}_{\check{\mathcal{N}}}(\operatorname{Locsys}_{\check{G}}(\Sigma)).$$

This is a categorical form of the Betti geometric Langlands correspondence, relating sheaves with nilpotent singular support on the moduli of $G$-bundles to ind-coherent sheaves with nilpotent singular support on the moduli of dual-group local systems. The source attributes the proposal to Ben-Zvi and Nadler; its resolution status is not specified here.