[v1.x] Deflake the child process cleanup tests #4296

Job	Run time
checks / pre-commit	36s
checks / doc-snippets	12s
checks / test (3.11, highest, windows-latest)	3m 28s
checks / test (3.10, highest, windows-latest)	2m 40s
checks / test (3.12, highest, ubuntu-latest)	47s
checks / test (3.13, lowest-direct, ubuntu-latest)	47s
checks / test (3.10, lowest-direct, windows-latest)	2m 29s
checks / test (3.10, highest, ubuntu-latest)	48s
checks / test (3.11, highest, ubuntu-latest)	46s
checks / test (3.11, lowest-direct, windows-latest)	2m 21s
checks / test (3.14, lowest-direct, windows-latest)	2m 14s
checks / test (3.13, lowest-direct, windows-latest)	2m 39s
checks / test (3.13, highest, ubuntu-latest)	46s
checks / test (3.13, highest, windows-latest)	6m 1s
checks / test (3.12, highest, windows-latest)	2m 35s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 5s
checks / test (3.14, highest, ubuntu-latest)	1m 14s
checks / test (3.14, highest, windows-latest)	2m 14s
checks / test (3.10, lowest-direct, ubuntu-latest)	49s
checks / test (3.12, lowest-direct, windows-latest)	2m 37s
checks / test (3.12, lowest-direct, ubuntu-latest)	52s
checks / test (3.11, lowest-direct, ubuntu-latest)	47s
all-green	4s
	38m 51s

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