Culture and Approval bonuses are not identified on tool tips that I have seen.
Approval at least was working in a prior beta, but I think it got broke when Beta 4 dropped. I know for a fact that Approval Relics aren't working for me in my games, as I tested it by setting up a planet with max population that had less than 100% approval (so I knew the Approval couldn't change from population growth) and then hooking up an Approval Relic. No change in approval in the slightest the next turn.
Before anyone asks, yes, I've already submitted a ticket regarding this. 