When running an adaptive test on a page the publish status and test status fields do not change/update after the test is complete. So any page that has ran an adaptive test always shows. Submitted a ticket but support responded and suggested submitting an idea here.
Published status labels. You’re right that the “Published A/B” status persisting after a test ends, and the lack of an “active test” indicator for adaptive tests, are confusing UX issues. I’ve documented both of these as separate pieces of feedback for our product team.