Rewrite TestChildProcessCleanup with socket-based deterministic liveness probe #1427

Job	Run time
checks / readme-snippets	11s
checks / pre-commit	37s
checks / test (3.10, locked, ubuntu-latest)	51s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 3s
checks / test (3.10, lowest-direct, windows-latest)	2m 35s
checks / test (3.11, locked, windows-latest)	2m 35s
checks / test (3.11, lowest-direct, ubuntu-latest)	54s
checks / test (3.10, locked, windows-latest)	2m 20s
checks / test (3.11, lowest-direct, windows-latest)	3m 1s
checks / test (3.14, locked, ubuntu-latest)	2m 26s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 4s
checks / test (3.11, locked, ubuntu-latest)	54s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 21s
checks / test (3.13, lowest-direct, ubuntu-latest)	53s
checks / test (3.14, locked, windows-latest)	3m 14s
checks / test (3.13, locked, ubuntu-latest)	49s
checks / test (3.12, locked, windows-latest)	3m 46s
checks / test (3.13, lowest-direct, windows-latest)	2m 44s
checks / test (3.12, lowest-direct, windows-latest)	3m 39s
checks / test (3.13, locked, windows-latest)	2m 19s
checks / test (3.12, locked, ubuntu-latest)	56s
checks / test (3.14, lowest-direct, windows-latest)	3m 20s
all-green	4s
	41m 36s

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