feature: Cache for the file handler to avoid stat()ing on every request

This issue comes from readme.md.

@krig you migh add some infos details about it. :rocket:

Start by reading readme.md and locating the file handler described there. Determine how requests currently trigger stat() and what cache behavior the issue expects. The work is done when the handler avoids stat() on every request while preserving correct file-serving behavior, with validation added where the repository's existing tests or checks support it.

Written by the indexing model from the issue text.