Rewrite TestChildProcessCleanup with socket-based deterministic liveness probe #1408

Job	Run time
checks / pre-commit	40s
checks / readme-snippets	13s
checks / test (3.10, locked, windows-latest)	2m 18s
checks / test (3.11, lowest-direct, windows-latest)	3m 32s
checks / test (3.10, locked, ubuntu-latest)	54s
checks / test (3.11, locked, ubuntu-latest)	49s
checks / test (3.11, lowest-direct, ubuntu-latest)	50s
checks / test (3.10, lowest-direct, windows-latest)	2m 30s
checks / test (3.13, lowest-direct, windows-latest)	2m 43s
checks / test (3.10, lowest-direct, ubuntu-latest)	57s
checks / test (3.14, lowest-direct, windows-latest)	2m 32s
checks / test (3.13, locked, windows-latest)	2m 26s
checks / test (3.12, locked, windows-latest)	3m 27s
checks / test (3.14, locked, ubuntu-latest)	2m 25s
checks / test (3.13, lowest-direct, ubuntu-latest)	58s
checks / test (3.12, lowest-direct, ubuntu-latest)	59s
checks / test (3.12, locked, ubuntu-latest)	58s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 18s
checks / test (3.13, locked, ubuntu-latest)	51s
checks / test (3.14, locked, windows-latest)	3m 46s
checks / test (3.12, lowest-direct, windows-latest)	3m 58s
checks / test (3.11, locked, windows-latest)	2m 25s
all-green	3s
	41m 32s

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