They've changed it up a bit. Library is now where you see your Watch Later playlist and purchases. I believe Favorites and Liked Videos is also located in the Library under something like Created Playlists or something like that. I'm not at home right now so I'm just going off of memory. Why there's nothing in your History, I can't say.
Signed Out, Signed In, Cleared History, Cleared Cookies. Still liked vids don't get added to Library OR History. The only thing the app remembers is my subscriptions and my searchs.