  For the integral canonical model $\mathscr{S}_{\mathsf{K}^p}$ of a Shimura
variety $\mathrm{Sh}_{\mathsf{K}_0\mathsf{K}^p}(\mathbf{G},\mathbf{X})$ of
abelian type at hyperspecial level $K_0=\mathcal{G}(\mathbb{Z}_p)$, we
construct a prismatic $F$-gauge model for the `universal'
$\mathcal{G}(\mathbb{Z}_p)$-local system on
$\mathrm{Sh}_{\mathsf{K}_0\mathsf{K}^p}(\mathbf{G},\mathbf{X})$. We use this to
obtain new $p$-adic information about these Shimura varieties, notably an
abelian-type analogue of the Serre--Tate theorem (realizing an expectation of
Drinfeld in the abelian-type case) and a prismatic characterization of these
models. To do this, we make several advances in integral $p$-adic Hodge theory,
notably the development of an integral analogue of the functor
$D_{\mathrm{crys}}$.
