Ramified trace conjecture for enhanced automorphic sheaves

Let $X$ be a smooth complete curve, let $G$ be reductive, let $\ul{x}$ be a finite set of points, and let $\operatorname{Isoc}_G$ be the stack of $G$-isocrystals. Let $\operatorname{Autom}(X,G)^{\operatorname{enh}_{\ul{x}}}$ be the enhanced automorphic object, and let $\operatorname{cl}(\ul{\operatorname{Shv}}_{\operatorname{HL}}(\operatorname{Bun}_G^{\operatorname{level}_{\ul{x}}}),\operatorname{Frob})$ be the Frobenius class of the Hecke-lisse object. Ramified trace conjecture. There exists a canonical isomorphism in $\operatorname{Shv}(\operatorname{Isoc}_G)$:

$$\operatorname{Autom}(X,G)^{\operatorname{enh}_{\ul{x}}}\simeq \operatorname{cl}(\ul{\operatorname{Shv}}_{\operatorname{HL}}(\operatorname{Bun}_G^{\operatorname{level}_{\ul{x}}}),\operatorname{Frob}).$$

This generalizes the unramified trace comparison to the ramified setting; the source gives no resolution evidence.