Log-prismatic extension conjecture after semistable alteration

Let $\operatorname{Spf}(A)$ be an affine smooth $p$-adic formal scheme over $\operatorname{Spf}(\mathcal{O}_{\breve{E}})$, and let

$$\mathcal{N}\in \operatorname{Vect}(A_{\mathrm{qsyn}},\mathbbl{\Delta}_{\bullet}[1/(p,I)])$$

be a finite locally free crystal. A morphism $g\colon \operatorname{Spf}(A')\rightarrow \operatorname{Spf}(A)$ is required to be a composition of a rig-étale morphism followed by an admissible blow-up, with $\operatorname{Spf}(A')$ semistable over $\operatorname{Spf}(\mathcal{O}_{\breve{E}})$.

Log-prismatic extension conjecture. There exists such a morphism

$$g\colon \operatorname{Spf}(A')\rightarrow \operatorname{Spf}(A)$$

and a finite locally free log-prismatic crystal

$$\mathcal{M}\in \operatorname{Vect}(\operatorname{Spf}(A')_{\mathbbl{\Delta}_{\log}},\mathcal{O}_{\mathbbl{\Delta}_{\log}})$$

which extends $\mathcal{N}$.

This is an extension statement for finite locally free prismatic crystals after a semistable alteration. The source supplies no resolution status, so it is recorded as open.