Berkovich's henselization conjecture for formal schemes

Let $k$ be a valued field, let $\mathfrak X$ be locally of the form $\operatorname{Spf}(\mathcal A^\circ)$ for $k$-affinoid algebras $\mathcal A$, so that $\mathfrak X$ is of finite type over $k^\circ$ and is normal in its generic fiber, and let $Z\hookrightarrow\mathfrak X_s$ be a closed subscheme. Write $(\widehat{\mathfrak X}_Z)_\eta$ for the generic fiber of the formal completion of $\mathfrak X$ along $Z$. Berkovich's henselization conjecture. The henselization of $\mathfrak X$ along $Z$ is completely determined by the generic fiber $(\widehat{\mathfrak X}_Z)_\eta$. The conjecture asks whether this generic fiber retains precisely the information about the formal scheme needed to recover its henselization along the special-fiber subscheme $Z$; no resolution is supplied in the source.