A shopper sends a link to a friend: 'this one is cheaper at the other chain'. If the friend has the app, the link should open the product. If not, it should open the store, and after the install it should still open the product. That last part is what deep linking is really about.
AppsFlyer carries the link through the install. The app receives a payload with the product id and, whatever the path, hands it to the same router as every other navigation, so a link is just one more way to arrive at the product page. The page loads its data from the store like any other visit and does not care how it was opened.
Two details need care. A link can arrive before the user is signed in, so the destination is remembered until sign-in with Google or Apple is done. And a link can point at a product that no longer exists, which should land on a calm message and the search box, never on a blank screen. Test the cold start, the warm start and the first run after install separately: they are three different code paths.