Here are the steps to transfer your backup from one device to another:
Make a backup
iOS/Android: tap on Settings/Backup (or in the old versions, More/Backup)
Mac OS: File > Backup
Windows (WSA Android): Click on Settings/Backup, more information here
Save the backup file to your cloud storage (Dropbox, Box, Apple (iCloud) Files, Google Drive, OneDrive ...)
or email it to yourself.
(Recommended:  keep it as an archive so your songs are safe; Recommended: occasionally do backups in iReal Pro in case of hardware failure, resetting, loss, damage etc.)
Apple users can use Airdrop to transfer songs between iOS and Mac devices.
Windows (WSA) by default saves it to your Windows Downloads folder.
Import the backup – songs and playlists: (requires iReal Pro 5.0.4 or higher)   
iOS: In Dropbox tap on the BACKUP.html file, on the top right, tap on Share, Export, Open in and select Import with iReal Pro. In Mail, tap and hold the BACKUP.html file and choose Copy to iReal Pro.
OS X: drag and drop the BACKUP.html file over the iReal Pro app icon in the dock of your computer.
Android: From the cloud, open the BACKUP.html file with iReal Pro. Import from Dropbox or Drive information here. From Email, touch the Backup file name itself to import.
(You can also touch the Download icon to Save to internal memory, or touch the Drive icon to save to your Drive cloud storage.)