Make sure your backup is completing successfully. You need as much free space for the Full Backup, as the entire ST3 install with all its audio files. If you have 10GB of audio files, your backup files will be about 10GB.
Assuming the backup is actually viable, then make sure the file has transferred successfully. Cloud transfers can be unreliable for a file that big. AirDrop will be more reliable, but slow. A USB drive is often the best, fastest, most reliable method (plus gives you another backup location).
Then when restoring, you'll need as much free space as the backup file. 10GB file, you'll need at least 10GB free space to restore that into ST4.