test: migrate stale os.kill monkeypatches to gateway.status._pid_exists

PR #21561 migrated liveness probes across 14 call sites from
`os.kill(pid, 0)` to `gateway.status._pid_exists` (psutil-first) so
the gateway doesn't Ctrl+C-itself on Windows via bpo-14484. A handful of
tests still patched the old `os.kill` seam and either happened to pass
on POSIX (when PID 12345 incidentally wasn't alive on the CI worker) or
failed outright — on CI runs they surfaced as 7 flaky/stable failures.

Migrate each affected test to patch the correct seam:

- tests/tools/test_browser_orphan_reaper.py (5 tests)
    Patch `gateway.status._pid_exists` instead of `os.kill`.
    Rename test_permission_error_on_kill_check_skips to
    test_alive_legacy_daemon_is_reaped — the old assertion was
    "PermissionError on sig 0 → skip dir"; post-migration the
    untracked-alive-daemon path always reaps the dir after SIGTERM
    (best-effort semantics were preserved).

- tests/tools/test_windows_native_support.py (4 tests)
    Replace tests that asserted `os.kill` seam behavior with tests
    that exercise `ProcessRegistry._is_host_pid_alive` as a
    delegator and split out a new TestPidExistsOSErrorWidening class
    that hits `gateway.status._pid_exists` directly via the POSIX
    fallback branch (so Windows-style `OSError(WinError 87)` + `PermissionError`
    widening is still covered on Linux CI).

- tests/tools/test_process_registry.py (1 test)
    Mock `psutil.Process` + `_pid_exists` instead of `os.kill`
    for the detached-session kill path.

- tests/tools/test_mcp_stability.py::test_kill_orphaned_uses_sigkill_when_available
    SIGTERM → alive-check → SIGKILL flow now uses `_pid_exists`
    for the middle step; assertion count drops from 3 to 2.

- tests/gateway/test_status.py::TestScopedLocks (2 tests)
    `acquire_scoped_lock` consults `_pid_exists`; patch that
    seam directly instead of trying to control the nested psutil
    call via os.kill monkeypatch.

- tests/hermes_cli/test_gateway.py::test_stop_profile_gateway_keeps_pid_file_when_process_still_running
    The stop loop sends one SIGTERM via os.kill then polls 20x via
    _pid_exists; instrument both separately. Old assertion
    `calls["kill"] == 21` split into `kill == 1` + `alive_probes == 20`.

- tests/hermes_cli/test_auth_toctou_file_modes.py::test_shared_nous_store_writes_0o600_with_0o700_parent
    Commit c34884ea2 switched the pytest seat-belt guard in
    `_nous_shared_store_path()` from `Path.home() / ".hermes"`
    to `get_default_hermes_root()`, which honors HERMES_HOME. The
    test sets both HERMES_HOME and HERMES_SHARED_AUTH_DIR to
    subpaths of the same tmp_path, and the override now collapses
    onto the same path the guard is refusing. Renamed the override
    subdirectory so the two paths diverge — guard passes, test runs.

All 21 original CI failures and their local-flaky siblings now pass
(278 tests across the touched files, 0 failures).

tests/tools/test_mcp_stability.py

@@ -130,15 +130,18 @@ class TestStdioPidTracking:
         fake_sigkill = 9
         monkeypatch.setattr(signal, "SIGKILL", fake_sigkill, raising=False)
 
+        # Post-#21561 the alive check routes through
+        # ``gateway.status._pid_exists`` (so it's safe on Windows — see
+        # bpo-14484). Return True so the SIGKILL escalation fires.
         with patch("tools.mcp_tool.os.kill") as mock_kill, \
+             patch("gateway.status._pid_exists", return_value=True), \
              patch("time.sleep") as mock_sleep:
             _kill_orphaned_mcp_children()
 
-        # SIGTERM, then alive-check (signal 0), then SIGKILL
+        # SIGTERM then SIGKILL; the alive check no longer touches os.kill.
         mock_kill.assert_any_call(fake_pid, signal.SIGTERM)
-        mock_kill.assert_any_call(fake_pid, 0)  # alive check
         mock_kill.assert_any_call(fake_pid, fake_sigkill)
-        assert mock_kill.call_count == 3
+        assert mock_kill.call_count == 2
         mock_sleep.assert_called_once_with(2)
 
         with _lock: