Apple’s implementation of enabling access to files is entirely different. I actually much prefer it because it sidesteps the self-dealing permissions bomb that Google just set off.
In iOS, applications can use the File Provider API to present themselves in the Files app. You can move/copy/delete data there using the normal human interface constructs native to iOS, including mouse support and keyboard shortcuts on iPadOS.
Apps can also present the same directory internally (inside the app). Cloud-backed applications can then do useful things like materialization, eviction, and dataless file presence.
It doesn’t allow standing access to the entire filesystem, though. iOS only has support for applications reading outside their sandbox if the apps are from the same developer, and then they can call a pooled storage location for all apps that share the same “Team ID” (e.g., top level developer account/organization).
It’s actually far easier (functionally) to grant access to your entire photo library, so for example you can have an app query and backup your photo library.
“True” filesystem-wide backup requires hooking into the iOS backup/MobileFile hooks. Apple isn’t as hostile to third parties doing that as Google is to anyone accessing their own device data. But the process is more cumbersome by far.