I don’t think this is accurate, actually:
Memory space: Mobile OSes unload inactive apps from memory when memory is needed, so more apps don’t really take up more memory. It’s possible you meant disk space, in which case yes, they do, but with 30 apps installed that’s still generally going to be a small fraction of a 64GB flash storage.
Background processes: At least on iOS (and I think to some degree on Android) apps are extremely limited in what they’re permitted to do in the background and when.
Push notifications: The “push” refers to the fact that notifications are pushed from servers to the phone without the app having to check for them. In many cases, the app isn’t even involved once the notification gets to the device: the OS just displays it.