tests

chore: add check for closed connector #4688

Job	Run time
unit tests (3.13)	55s
unit tests (3.9)	56s
integration tests (windows-latest, 3.9)	42s
integration tests (macos-latest, 3.9)	46s
integration tests (windows-latest, 3.13)	43s
integration tests (macos-latest, 3.13)	46s
integration tests (ubuntu-latest, 3.9)	55s
integration tests (ubuntu-latest, 3.13)	56s
	6m 39s

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