Restoring App Data from Backup
It turns out that the files stored in Readdle Documents are not stored in the normal location where apps store their Documents and Data. (This may be because Readdle Documents lists itself as a Cloud Storage Provider.) Using the Tree View of the Raw Files section of iBackup Viewer, I was able to export the files in the AppDomainGroup-group.com.readdle.documents/File Provider Storage folder and reupload the files into Readdle Documents through its WebDAV feature.

I downloaded iBackup Viewer from https://www.imactools.com/iphonebackupviewer/.