Apps cannot run constantly in the background, they're very much at the whim of the Operating System and must register background operations and complete them usually in ~30s before being killed.
They also can't collect any information in the background they couldn't in the foreground. Like apps can't tell which apps you open, can't tell what info you put into other apps, can't track you across other apps etc.
Actually upon further looking at the docs I don't think they can collect any information in the background.
Like the app has to register as being allowed in background mode, upon which if a push notification is sent to it the OS wakes it up for ~30 seconds to make an API call or set data. But there's no UI shown, there's no ability to track which app is open, or even if the device is awake or asleep. It's not like the apps are able to run code in the background whenever they choose.
not including apps with Allow in Background location permission, like bicycle tracking apps etc. but those are done with explicit permission from the user.
In what way?
What information can a native app get from a user that a website couldn't?