Rewrite TestChildProcessCleanup with socket-based deterministic liveness probe #1393

Job	Run time
checks / readme-snippets	11s
checks / pre-commit	40s
checks / test (3.11, lowest-direct, windows-latest)	3m 40s
checks / test (3.11, lowest-direct, ubuntu-latest)	51s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 0s
checks / test (3.12, locked, ubuntu-latest)	58s
checks / test (3.11, locked, ubuntu-latest)	52s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 2s
checks / test (3.13, locked, windows-latest)	2m 40s
checks / test (3.12, lowest-direct, windows-latest)	3m 38s
checks / test (3.12, locked, windows-latest)	4m 5s
checks / test (3.13, locked, ubuntu-latest)	45s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 18s
checks / test (3.14, locked, ubuntu-latest)	2m 22s
checks / test (3.10, lowest-direct, windows-latest)	2m 41s
checks / test (3.13, lowest-direct, windows-latest)	2m 40s
checks / test (3.14, locked, windows-latest)	3m 7s
checks / test (3.10, locked, windows-latest)	2m 25s
checks / test (3.11, locked, windows-latest)	2m 35s
checks / test (3.14, lowest-direct, windows-latest)	2m 15s
checks / test (3.13, lowest-direct, ubuntu-latest)	51s
checks / test (3.10, locked, ubuntu-latest)	55s
all-green	3s
	41m 34s

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