Embedded resolution of singularities for quasi-excellent regular schemes

Let $X\subset Z$ be a reduced closed subscheme of a quasi-excellent regular Noetherian scheme $Z$. Write $X'$ for the strict transform of $X$ under a proper birational morphism $\pi:Z'\to Z$, and write $\operatorname{Sing}(X)$ for the singular locus of $X$. Embedded resolution of singularities. There exist a regular scheme $Z'$ and a proper, birational morphism $\pi:Z'\to Z$ such that

$$\begin{gathered} X'\subset Z'\text{ is regular},\\ \pi^{-1}(Z\setminus\operatorname{Sing}(X))\cong Z\setminus\operatorname{Sing}(X),\\ \pi^{-1}(\operatorname{Sing}(X))_{\mathrm{red}}\text{ is a simple normal crossing divisor,}\ \end{gathered}$$

where each irreducible component of the divisor is regular, its components intersect transversally, and it intersects $X'$ transversally. Thus the singularities of $X$ admit an embedded resolution by a proper birational modification that is an isomorphism away from the singular locus. The statement is presented as the characteristic-zero-style resolution goal for classes of singularities in general, including positive or mixed characteristic; the supplied context does not establish whether it is known or remains open in the stated generality.