should I care about closing/cancelling channel during object teardown if it's used only internally in the object and coroutine scope to operate it was already cancelled?

Since the coroutine which is using to operate that is also cancelled and you are sure that that channel is no longer being used, I think you don't need to care about it

Channels are a communication primitive between coroutines, but need not to be closed if the coroutines are no longer active. Closing a channel is useful for other things, but is not necessary in your case.