The readme in botan-sys suggests that if botan headers can be found in foo/botan-3/botan, BOTAN_INCLUDE_DIR should only be set to foo/, implying that the botan-3/botan path will be added by the build system.
Currently, for the default search paths, the botan-{major-version} suffix is appended to the basepath, but not to BOTAN_INCLUDE_DIR if it is set, i.e. it would need to be set to foo/botan-3, which does not adhere to the readme.

I've provided a draft implementation that searches in BOTAN_INCLUDE_DIR/botan-{3,2} just like it does for the default paths.

That however would prohibit the user to provide things such as foo/botan/ for the BOTAN_INCLUDE_DIR, where the headers are directly contained in foo/botan/, so the simpler fix could just be to update the readme :)