The Session management mismatch for ID is intentional for security reasons. Even if you are logged in on play, the same is not true for ID.
You can opt for the “Remember Me” option to persist your log in, but ID is by design not supposed to retain any session for too long without requesting authentication again.
As for the UI, I understand what you mean and will update it with your considerations in mind.
Do let us know of anything else, your feedback is most appreciated!