tests

chore: add check for closed connector #4788

Job	Run time
unit tests (3.9)	1m 1s
unit tests (3.13)	1m 3s
integration tests (macos-latest, 3.13)	1m 28s
integration tests (ubuntu-latest, 3.13)	53s
integration tests (windows-latest, 3.9)	1m 32s
integration tests (macos-latest, 3.9)	1m 47s
integration tests (windows-latest, 3.13)	1m 48s
integration tests (ubuntu-latest, 3.9)	55s
	10m 27s

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