To backup to iCloud, first, you will want to make sure you have the Files app downloaded onto your device. Then you can go into OnSong > Tap Share Menu > Export - tap the folder icon > Select Files > OnSong Backup > Export > Select iCloud Drive -If you have a specific folder created you can then tap that, if not... > Tap Add.
By the way, you can do all of your exporting this way... not just for backups.
You can also import from iCloud as well, either directly from the app itself or if you go into OnSong > Tap Songs > All Songs > "+" Sign > Import/Files > Select content > Import.