LaTeX is extremely slow if many small files are processed – the problem seems
to be that it keeps searching up files without caching them.

I think the fix is the following (merged):
https://github.com/latex3/latex2e/pull/1063

Please consider applying. For the news file, included in the commit:

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\section{Code improvements}

\subsection{Performance in checking file existence}

The additon of hooks, etc., to file operations had a side-effect in that
multiple checks were made that the file existed. In larger documents using
lots of files, these filesystem operations caused non-trivial performance
impact. We now cache the existence of files, such that these repeated
filesystem
calls are avoided.
----------------------------------------------