close() escalated to kill_process_tree() but never imported it; the NameError
was swallowed by contextlib.suppress, so on the TimeoutExpired path neither the
kill nor the post-kill wait ran and a root codex ignoring SIGTERM leaked (a
regression vs the previous self._proc.kill()). Import it from agent.deadline
and add a test forcing the timeout path that asserts the tree kill and the
follow-up wait both run. Also drop the upstream product reference from the
test docstring (credit stays in the PR body) and pass encoding= to the PID
file reads flagged by the Windows footgun scanner.