tests

chore: add check for closed connector #5671

Job	Run time
unit tests (3.13)	1m 10s
integration tests (ubuntu-latest, 3.9)	1m 6s
integration tests (macos-latest, 3.13)	1m 27s
unit tests (3.9)	1m 10s
integration tests (ubuntu-latest, 3.13)	1m 16s
integration tests (windows-latest, 3.13)	1m 47s
integration tests (windows-latest, 3.9)	1m 33s
integration tests (macos-latest, 3.9)	1m 51s
	11m 20s

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