Rewrite TestChildProcessCleanup with socket-based deterministic liveness probe #1407

Job	Run time
checks / pre-commit	34s
checks / readme-snippets	14s
checks / test (3.10, locked, windows-latest)	2m 17s
checks / test (3.11, locked, ubuntu-latest)	49s
checks / test (3.14, locked, ubuntu-latest)	2m 23s
checks / test (3.13, lowest-direct, windows-latest)	2m 49s
checks / test (3.12, locked, ubuntu-latest)	53s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 22s
checks / test (3.14, lowest-direct, windows-latest)	2m 30s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 2s
checks / test (3.12, lowest-direct, windows-latest)	3m 45s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 1s
checks / test (3.14, locked, windows-latest)	3m 44s
checks / test (3.11, lowest-direct, windows-latest)	2m 52s
checks / test (3.11, locked, windows-latest)	2m 33s
checks / test (3.13, lowest-direct, ubuntu-latest)	51s
checks / test (3.10, locked, ubuntu-latest)	50s
checks / test (3.13, locked, windows-latest)	2m 18s
checks / test (3.13, locked, ubuntu-latest)	48s
checks / test (3.10, lowest-direct, windows-latest)	2m 21s
checks / test (3.12, locked, windows-latest)	3m 21s
checks / test (3.11, lowest-direct, ubuntu-latest)	54s
all-green	5s
	40m 16s

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