Rewrite TestChildProcessCleanup with socket-based deterministic liveness probe #1395

Job	Run time
checks / pre-commit	31s
checks / readme-snippets	14s
checks / test (3.12, lowest-direct, windows-latest)	3m 55s
checks / test (3.10, locked, ubuntu-latest)	52s
checks / test (3.13, locked, ubuntu-latest)	50s
checks / test (3.13, lowest-direct, ubuntu-latest)	54s
checks / test (3.12, locked, windows-latest)	3m 20s
checks / test (3.14, lowest-direct, ubuntu-latest)	17s
checks / test (3.11, lowest-direct, ubuntu-latest)	56s
checks / test (3.13, lowest-direct, windows-latest)	2m 24s
checks / test (3.12, locked, ubuntu-latest)	1m 3s
checks / test (3.11, locked, windows-latest)	2m 29s
checks / test (3.10, locked, windows-latest)	2m 34s
checks / test (3.12, lowest-direct, ubuntu-latest)	59s
checks / test (3.10, lowest-direct, windows-latest)	2m 45s
checks / test (3.13, locked, windows-latest)	2m 44s
checks / test (3.11, locked, ubuntu-latest)	52s
checks / test (3.14, lowest-direct, windows-latest)	2m 27s
checks / test (3.14, locked, windows-latest)	3m 18s
checks / test (3.14, locked, ubuntu-latest)	2m 19s
checks / test (3.10, lowest-direct, ubuntu-latest)	58s
checks / test (3.11, lowest-direct, windows-latest)	2m 36s
all-green	5s
	39m 22s

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