Potent categorical Langlands duality for reductive groups

Let $G$ be a reductive group and let $\check G$ be its Langlands dual group. Denote by $\mathcal{H}_G^{dR}$ and $\mathcal{H}_{\check G}^{dR}$ the de Rham potent Hecke monads, and by $G\operatorname{-cat}^{pot,dR}$ and $\check G\operatorname{-cat}^{pot,dR}$ the corresponding de Rham potent categorical representation categories. Potent categorical Langlands duality. The multiplicative 2-Fourier transform identifies $\mathcal{H}_G^{dR}$ with $\mathcal{H}_{\check G}^{dR}$, and consequently there is an equivalence

$$G\operatorname{-cat}^{pot,dR}\simeq \check G\operatorname{-cat}^{pot,dR}.$$

This is the main conjectural extension of multiplicative 2-Fourier duality from tori to general reductive groups. The source further predicts a single Hecke monad over $\mathfrak{t}/\Lambda\times\check{\mathfrak{t}}/\check\Lambda$ from which various Hecke categories arise, as well as analogous Betti and graded statements.