iOS has 2 solutions to this. They have a push models where you “share” the file to the next app you want to use. And they also have a traditional file store model where all apps can request to save and request to load files.

Critically, apps can not directly read your files, they can show a button which will open the OS file picker and the user can pick a file to open which then provides access to the app.

This means that opening a game does not instantly expose all of your sensitive files.