This compiles as I would expect:
%\DocumentMetadata{}
\documentclass{article}
\usepackage{enumext}
\begin{document}
\begin{enumext}
\item One
\begin{enumext}
\item One
\item Two
\end{enumext}
\item Two
\item Three
\begin{enumext*}[columns=2]
\item One
\item Two
\end{enumext*}
\end{enumext}
\end{document}
When \DocumentMetadata is included, however, the nested {enumext*} starts one number higher.

This compiles as I would expect:
When
\DocumentMetadatais included, however, the nested{enumext*}starts one number higher.