There was no BackHandler anywhere, so Back was left entirely to the system, which finishes the activity rather than navigating up a folder or closing a viewer. Verified on the phone: Back on the roots screen still exits, and Back inside a folder now goes up and stays in the app.
The handler has to sit above the overlay branch, not after it: that branch returns early, so anything below it is never composed while a viewer or the editor is open, which is precisely when Back most needs an answer. The first attempt made that mistake and the device test caught it.
SoftwareApp
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