tests

chore: add check for closed connector #4687

Job	Run time
integration tests (macos-latest, 3.13)	2m 33s
unit tests (3.9)	2m 43s
unit tests (3.13)	2m 43s
integration tests (windows-latest, 3.9)	1m 52s
integration tests (macos-latest, 3.9)	1s
integration tests (ubuntu-latest, 3.9)	1m 2s
integration tests (ubuntu-latest, 3.13)	57s
integration tests (windows-latest, 3.13)	2m 0s
	13m 51s

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