Environment

• Hermes Agent v0.10.0 (2026.4.16)
• OS: Windows 11
• Python: 3.11.15

Summary

On Windows, os.kill(pid, 0) raises OSError: [WinError 87] ERROR_INVALID_PARAMETER for non-existent PIDs, not ProcessLookupError as on POSIX. Several liveness checks only catch (ProcessLookupError, PermissionError), so a stale gateway.pid file from a previous run makes hermes gateway run crash before the gateway can start.

Reproduce

1. On Windows, run hermes gateway run, then kill the process (or reboot) so that %LOCALAPPDATA%\hermes\gateway.pid is left behind referencing a PID that no longer exists.
2. Run hermes gateway run again.

Actual

```
File "...\gateway\status.py", line 578, in get_running_pid
os.kill(pid, 0)
OSError: [WinError 87] 参数错误。
```

Additional identical failures surface downstream once the first one is fixed:

• `gateway/status.py:343` in `acquire_scoped_lock` — breaks Telegram connect (`[Telegram] Failed to connect to Telegram: [WinError 87]`)
• `tools/process_registry.py:258` in `_is_host_pid_alive` — logged as `"Process checkpoint recovery: [WinError 87]"`
• `gateway/run.py:10318` — `--replace` wait loop would hang/crash on a dead PID

Expected

Stale/non-existent PIDs on Windows are treated as "process not found", the stale pid/lock files are cleaned up, and the gateway starts normally.

Root cause

Python docs note that on Windows `os.kill` signals invalid PIDs via `OSError` (errno 22 / WinError 87), not `ProcessLookupError`. The existing handlers are POSIX-only.

Suggested fix

Add `except OSError` (treat as "process gone" + cleanup) alongside the existing `except (ProcessLookupError, PermissionError)` at:

• `gateway/status.py:578` (`get_running_pid`)
• `gateway/status.py:343` (`acquire_scoped_lock`)
• `gateway/run.py:10318` (replace-wait loop)
• `tools/process_registry.py:258` (`_is_host_pid_alive`)

Each site is a one-line addition mirroring the existing cleanup branch. Verified locally on Windows 11 — gateway starts cleanly after applying these four changes. Happy to open a PR if useful.