#63955 made Hermes survive a broken `bash -l` (Ainz's `Directory
\drivers\etc does not exist`) by falling back to non-login `bash -c`.
But a non-login shell never sources /etc/profile, so it never gets
`…\usr\bin` on PATH — and that dir holds every coreutil the file/terminal
tools shell out to (cat, mktemp, mv, wc, head, stat, chmod, mkdir, find).
Result: `write_file` returned bytes_written:0 with an EMPTY error (the
failure text went to a missing binary's stderr) and terminal commands
exited 127. The survive-broken-login-bash fix was only half-done: it
stopped crashing but silently failed every write.
Derive Git Bash's bin dirs (mingw64/bin, usr/bin, bin, …) from the
resolved bash.exe and prepend them to the subprocess PATH on Windows, in
/etc/profile precedence order so coreutils win over same-named System32
tools (find.exe, sort.exe) inside the shell. No-op off Windows and when a
login snapshot is healthy (the snapshot re-exports the full PATH inside
the shell), so this only bites on the broken-login fallback path.
Adds _git_bash_bin_dirs() (derivation, cached) + _prepend_git_bash_dirs()
(PATH merge), plus regression tests for PortableGit/MinGit layouts and
the run-env injection ordering.