Formally proper stack conjecture on mod-$p$ étale cohomology

Let $K$ be a finite extension of $\mathbb Q_p$, let $\mathcal O_K$ be its ring of integers, and let $\mathpzc X$ be a smooth formally proper stack over $\mathcal O_K$. Let $\widehat{\mathpzc X}$ be its $p$-adic completion, and let $\Upsilon_{\mathpzc X}$ be the natural comparison map. Formally proper stack conjecture.

$$\Upsilon_{\mathpzc X}\colon R\Gamma_{\mathrm{\acute et}}(\mathpzc X_{\mathbb C_p},\mathbb F_p)\longrightarrow R\Gamma_{\mathrm{\acute et}}(\widehat{\mathpzc X}_{\mathbb C_p},\mathbb F_p)$$

is an equivalence. This predicts mod-$p$ étale acyclicity for smooth formally proper stacks and would extend the comparison from the completion to the algebraic stack. The claim is presented as conjectural and is not resolved in the supplied text.