Yeah this seems like a huge oversight on iPadOS, particularly given the screen real estate available on the larger devices.
The app folders not being present is also odd.
Bill Standen
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Found the trigger, it's an iTerm2 thing.
Disable Enable session restoration under Preferences > Advanced > Session, after that you shouldn't have a problem.
Raised an issue with iTerm's developers. Not sure if there's something here on the OS side as well.