From the testing I've done, the best I can tell is that the files are stored within an internal storage used by the app.
You can save them to files by selecting them in the Inbox or Saved section and then use Share to send it to a file explorer app you have on your device. Then you can select the folder where you want to save them and then confirm.
Initial answer:
I would've posted this as a comment, but I don't have enough rep at the moment here.
I noticed you tagged this with Android 11. I know that Android 11 implemented some breaking changes to how storage access for apps works (see https://developer.android.com/about/versions/11/privacy/storage), so, without being able to test this at the moment, I wonder if the app in question just hasn't updated its logic to account for this.