So the result is that there was a track object in the database that did not belong to any song. The backup file contained this object in a way that prevented restoring the other track objects. I have hardened the backup creation to deal with this possible issue although I do not really know how this situation could develop in the first place.
My recommendation for anyone using multitrack files and audio regions would be to create a new full backup once version 3.6.10 is released because I can not rule out that this problem might occur for other users.