City State Bonuses - where can I see if they are applied?

City state bonuses come in two flavors. Permanent bonuses that improve districts or buildings and suzerain bonuses. These are independent.

Permanent bonuses are awarded for 1, 3 respectively 6 envoys to the city state. The type of bonus depends on the city state. There are 6 different types. Search your in-game Civilopedia (Use the question mark in the top right-hand corner to open the Civilopedia.) for "City-State Types" for an overview. These bonuses, once gained, are awarded until the city state is defeated, you loose envoys (the AI rarely uses the related spy missions) or you are at war with the city state.

Suzerain bonuses are awarded once you are suzerain. You don't need 6+ envoys. 3 suffice if no other civilization holds equal or more influence (envoys) over the city state. The bonus is active as long as you are suzerain. Check the Civilopedia for "Suzerain" for an explanation.

You can check your envoys and city-state bonuses using the city-state pane as shown in the screenshot below.

Using this panel, you can check the bonuses at each envoy level and for suzerainty by hovering over the respective text. See the images below.

As you can see in the last screenshot, I have 3+ envoys in each of the two commercial city-states which gives me +2 gold each to my lighthouse as you can see on the left. I hope this helps.