I can't tell whether a card is published or unpublished.
I presume you mean given it's also dependent on the publishing status of the stream. I'll explore a third visual state a card can be shown in to mean "publishing is just blocked by the stream not being public".
It would be nice if the eye toggle at least had a tooltip indicating current state. I realize I should be able to figure it out based on "It won't be published right away" above this box, but one forgets There is also the confusion of publishing a stream and then publishing a card -- is it a two or three step process to go live with a thought?
Most of the time a stream is already public and you're just adding thoughts. The "three step process" only happens if you're staging up cards for a stream you haven't made public yet.