tests

chore: add check for closed connector #4789

Job	Run time
unit tests (3.9)	1m 1s
unit tests (3.13)	1m 2s
integration tests (macos-latest, 3.9)	1m 43s
integration tests (ubuntu-latest, 3.9)	59s
integration tests (windows-latest, 3.9)	1m 25s
integration tests (windows-latest, 3.13)	1m 36s
integration tests (macos-latest, 3.13)	1m 43s
integration tests (ubuntu-latest, 3.13)	57s
	10m 26s

Provide feedback