The Windows branch of `_terminate_host_pid` early-returned after
`os.kill(pid, SIGTERM)` (which Python maps to `TerminateProcess` for
the target handle only), leaving descendant processes — e.g. Chromium
renderer/GPU/network helpers spawned by an `agent-browser` daemon —
running on Windows even after the preceding commit fixed POSIX.
The right Windows primitive is `taskkill /PID <pid> /T /F`:
`/T` walks the tree, `/F` force-terminates. Same approach
`gateway.status.terminate_pid(force=True)` already uses for the
gateway's own shutdown path; reuse the same shape here.
Why NOT extend the POSIX psutil tree-walk to Windows:
1. Windows doesn't maintain a Unix-style process tree. `psutil.
Process.children(recursive=True)` walks PPID links that go stale
when intermediate processes exit, so enumeration is best-effort
and silently misses orphaned descendants. The whole bug we're
fixing is orphaned descendants.
2. `psutil.Process.terminate()` on Windows is `TerminateProcess()`
for one handle — same single-PID scope as the existing
`os.kill`. The existing comment in `gateway/status.py::
terminate_pid` warns this explicitly: 'os.kill SIGTERM is not
equivalent to a tree-killing hard stop' on Windows.
3. Headless Chromium has no GUI window, so the softer
`taskkill /T` without `/F` (which sends WM_CLOSE) won't reach
it either. `/F` is required.
POSIX path is unchanged. The taskkill subprocess uses the same
`creationflags=windows_hide_flags()` pattern other Windows shellouts
in this codebase use. `FileNotFoundError` / `TimeoutExpired` /
`OSError` fall back to bare `os.kill(SIGTERM)` as cheap insurance.
Tests cover the Windows branch via the codebase's standard
`monkeypatch _IS_WINDOWS` pattern (`references/windows-native-
support.md`), plus POSIX tree-walk order, NoSuchProcess swallow,
and the OSError fallback path. 7 new tests, all green on Linux CI.
7ce6b504a2