Make iostream shutdown more robust #1856

Job	Run time
build (ubuntu-latest, 3.8)	3m 34s
build (ubuntu-latest, 3.11)	3m 42s
build (windows-latest, 3.8)	12m 23s
build (windows-latest, 3.11)	9m 30s
build (macos-latest, 3.8)	8m 42s
build (macos-latest, 3.11)	7m 5s
build (windows-latest, 3.9)	9m 49s
build (ubuntu-latest, pypy-3.8)	4m 16s
build (macos-latest, 3.10)	12m 1s
link_check	4m 21s
check_release	3m 9s
Make SDist	51s
test_docs	4m 14s
Test Lint	1m 27s
Test Minimum Versions	2m 47s
Test Prereleases	2m 13s
test_without_debugpy (ubuntu-latest, 3.9)	1m 39s
Install from SDist and Test	2m 18s
coverage	35s
tests_check	3s
	1h 34m 39s

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