During world showcase events if someone wants to check if the world they're at is currently Public, they'll probably look to the "Publish-date" label on the world's info page. However, this would not be what they looking for.

Currently the only find out if the world is public is if you try to favorite the world. The response you get will tell you. But what if you don't have an empty spot free to do this workaround?

In the Old menu, you'd know right away via "Unlisted" status.