This is a quick weekend hack that allows to sync photos to a Fritz! Box that unfortunately only offers FTP access. Other NAS systems offering FTP access should work as well.
First time usage: Go to settings and setup the URL of your NAS, your user name and your password. Then grant the app permissions to access your photos. Start the app, select which local album to sync and hit the sync button.
Files are copied if they don't exist on the target drive. To recover from interrupted uploads, files that have a different file size on the NAS will be overwritten by the local files.