This also kinda annoying..
In some games like ScourgeBringer, you can't even see the pop up greeting when you open the game (that "Hey there, your account name"), so I have no clue whether the Play Games is connected or not, thankfully it was not a hard or time consuming achievement that I missed.
To make sure it's connected, I have to change the setting:
Play Games app> setting> change account for games> select the specific game> ask each time.
This way, you'll be asked which account you gonna use every time you open the game, and if not, that means the game isn't connected to Play Games.