I had that before. It showed me as logged in but I couldn´t access anything. It cleared up when I added a sign-out button and signed out and in again. I think I caused the issue in the first place after I deleted some data tied to the app from the google play app in an attempt to remove my leaderboard score. In the end I could actually overwrite my old score with a much lower new one after doing this. (I couldn´t just reset the leaderboard in the dev console because it was already published) Reinstalling the app wasn´t enough to recover from this status.
So the steps to reproduce may be (I didn´t verify that)
1. Make app, sign in to google play
2. Delete the data tied to the app from the google play games app
3. Open the app again and it may end up in this werid state of showing to be "signed in" but unable to access any of the features (also the google play popup when signing in doesn´t appear)
4. Signing out and in again seems to solve it