I produced a fork of the Cygwin DLL in which the POSIX chdir() provides this same feature: the "currently logged drive" and per-drive current directory.

https://www.kylheku.com/cygnal/

It's behind quite a bit; haven't done a rebase in a while.

This is just one of the features (Issue 7); the idea is to provide a POSIX run-time for easily porting programs to Windows, but follow the conventions of the Windows environment.