You can copy your mp3 files in the Files app. Navigate to the source folder and select all files, then tap on "Move" and navigate to the Stage Traxx 3 folder. Then tap copy.
Here is a nice tutorial: https://www.lifewire.com/ios-files-app-4142651
It is possible that your backup is a full backup but then you created the backup when there was at most a single song in ST3. If you want you can email me that backup file and I can take a look at what type of backup it is exactly.
If it is a database only backup, you can then (after copying the mp3s) restore it and it will restore your lyrics and all other settings while keeping the mp3s that you copied. If it is a full backup it will delete the mp3s but I could change the backup type in that case if you send me the file.