"adjustbox" with Export option seems to break page selection (in "pdfpages")

Note the use of the undocumented feature of \includegraphics.

\documentclass{article}
\usepackage{pdfpages}
\newlength{\tempwidth}
\begin{document}
\settowidth{\tempwidth}{\includegraphics[page=1]{lipsum.pdf}}
\includepdf[fitpaper,pages=1,trim={0 0 {.5\tempwidth} 0},clip]{lipsum.pdf} % ***
\end{document}

The page key was unfortunately not supported by adjustbox till v1.1 from 2018/04/08. If you update to this version or a later one your code should start working.

Also trim={0 0 {.5\width} 0},clip can be shorten to Clip={0 0 {.5\width} 0} (note the uppercase 'C') if adjustbox is used with export or Export option.