Formal GAGA conjecture for good moduli spaces with affine diagonal

Let $\phi\colon \mathscr{X}\to \operatorname{Spec} A$ be a good moduli space morphism, where $A$ is a complete Noetherian local ring and $\phi$ is of finite type. Let $\widehat{\mathscr{X}}$ denote the formal completion of $\mathscr{X}$ along the closed point of $\operatorname{Spec} A$. The completion functor

$$\operatorname{Coh}(\mathscr{X})\to \operatorname{Coh}(\widehat{\mathscr{X}})$$

Formal GAGA conjecture. If $\mathscr{X}$ has affine diagonal, then the completion functor is an equivalence of categories.

This predicts formal GAGA for good moduli spaces under the affine-diagonal hypothesis. The surrounding discussion presents it as a consequence of the paper's local and global results, but the supplied text does not establish whether the assertion itself is proved or remains open.