Fix a "nice" curve $X$ (smooth, projective, proper, geometrically connected, what-have-you) and an algebraic torus $G$, both over a field of characteristic $0$ (possibly algebraically closed?).

From what I have been able to gather from several lecture videos by Gaitsgory (such as Gaitsgory - Singular support of coherent sheaves), the categorical-geometric Langlands Correspondence $G$ is supposed to be an equivalence of categories: $$\mathsf{DMod}\left(\mathsf{Bun}_G(X)\right) \cong \mathsf{QCoh}(\mathsf{LocSys}^{{}^LG}(X))$$ wherein $\mathsf{DMod}\left(\mathsf{Bun}_G(X)\right)$ is the ($\infty$-)category of D-modules on the moduli stack $\mathsf{Bun}_G(X)$ of $G$-bundles on $X$, and $\mathsf{QCoh}(\mathsf{LocSys}^{{}^LG})$ is the ($\infty$-)category of quasi-coherent modules on the stack of ${}^L G$-equivariant local systems on $X$, where ${}^L G$ is the Langlands dual of $G$.

My questions are then:

- Is this the correct statement? Specifically, I would like to understand if we need to replace $\mathsf{QCoh}$ with $\mathsf{IndCoh}$ (see part II of A study in derived algebraic geometry, Volume I: Correspondences and duality by Gaitsgory and Rozenblyum for an introduction to ind-coherent sheaves), and why (or why not)?
- What is a standard reference that I can consult? Most references that I have been able to find (by Gaitsgory, Laumon, etc.) are about the Langlands Correspondence for $\operatorname{GL}_2$, $\operatorname{GL}_n$, or more general kinds of reductive groups, and I don't think I have what it takes yet to extract the special case of tori from these papers.