new: Centralize file type stat-ing logic

This moves our logic to get a file's type into one function.  This has
several benefits: we can support OSes and file systems that do not
provide dirent.d_type or always return DT_UNKNOWN, complex
symlink-handling logic has been replaced by a simple stat fall-through
in one place, and the error message for un-stat-able file is more
accurate (previously, the error always mentioned directories, even
though a broken symlink is not a directory).