The PC Oculus app only accesses the PC (Rift) store; PC apps cannot be installed onto your Quest. These are separate from the native Quest apps; you can access the Quest store either in the headset (while not connected to a PC), on the website, or on the phone app. Both the website and the phone app can access the stores for all the different platforms (Quest, Rift, Go, and GearVR), so make sure you're on the right store before purchasing apps.
Some apps have both Quest and Rift versions, and some of these apps support cross-buy, meaning that buying one version will also get you the other version for free. You can check this store page to see if the app you bought on the Rift store has a cross-buy Quest version. If it does, you can claim the Quest version for free on the Quest store.