Condensed generalized Langlands parametrization for $\ell$-adic perverse sheaves

Let $n\geq 2$, let $X$ be a finite extension of a local nonarchimedean field, let $G(X)$ be a reductive group, and let $\mathrm{Gal}_{X,n}$ and $\mathrm{Weil}_{X,n}$ denote the corresponding $n$-fold coverings obtained by taking roots of cyclotomic characters up to order $n$. Let $G^\mathrm{dual}(\overline{\mathbb{Q}}_\ell)$ be the dual-group-valued target and let $\mathrm{Weil}_X$ be the Weil group of $X$. Condensed generalized Langlands conjecture. There are condensed parametrizations

$$\mathrm{Gal}_{X,n}\rightarrow G^\mathrm{dual}(\overline{\mathbb{Q}}_\ell)\times \mathrm{Weil}_X$$

and

$$\mathrm{Weil}_{X,n}\rightarrow G^\mathrm{dual}(\overline{\mathbb{Q}}_\ell)\times \mathrm{Weil}_X$$

for generalized $\ell$-adic perverse sheaves attached to $G(X)$. This is proposed as a generalization of the cited work of Fargues and Scholze to the covered Galois and Weil groups; the source does not provide a resolution.