test(antigravity): key the removed-home fixture off the platform's own home var

The effective-auth-type test asserts that a launch codeg cannot name a home
for reads as `Unreadable`, and expressed "no home" by blanking `HOME` in the
runtime env. `child_home_dir` reads `USERPROFILE` on Windows — the rule
`ntpath.expanduser` follows, which never consults `HOME` — so that entry was
never looked at: the home fell back to the runner's real profile, the
settings path resolved, and the absent file there read as `Absent`. The case
therefore only held on unix, and the Windows server cell failed on it.

The fixture now picks the key the same way production does, as the
`antigravity_settings_path_*` tests in the same module already do.