A web app doesn’t magically turn into a native app when you put it on the app store. The way it gets installed, and the system access is different, and better for stuff like notifications…
But the word “native” refers to applications made using the native SDK, which in Apple’s case is Swift. I’d be extremely impressed if the devs re-wrote the entire app in new code. But that would be unnecessary.
You can have non-native apps on the app store. A lot of your apps probably aren’t native. SDKs like flutter, used by liftoff and thunder, make development much easier in exchange for the resulting application running a bit less efficiently. Flutter applications can also run on both Android and iOS, and even desktop, with little additional work.