Following that logic, your phone is a browser and the apps are bookmarks with special permissions.
This is the case for many applications. Both major smartphone operating systems' included web browsers support progressive web applications (PWA). These use a service worker, a script cached on the device that acts as a proxy to cache a particular site's pages, scripts, and data and present them to the user even while the device is offline. They grant additional permissions to bookmarks on the device's home screen. For example, Safari for iOS allows a website added to the home screen to use the Push API to receive notifications through its service worker.
However, a lot of service providers maintain a native application for iOS and a native application for Android instead of relying on a PWA. Based on my recent conversation with UnknowingFool, this includes at least Grab, Doordash, Uber Eats, Instacart, Favor, Grubhub, and Postmates, and these providers are thought to have (unstated) good reasons for doing so.