How can I recover files from an incomplete iPad backup?

This whole situation has terribly affected my trust in apple. I had plans to replace my device I had no warnings that the backup was incomplete, and while replacing my device in store, the employee and i relied on this incomplete backup to transfer my data. If it had been a physical transfer, this never would have happened in the first place.

I have 22.7gb of incomplete data backed up to the cloud. It wasn’t able to transfer to a new device, of course, but i NEED a way to open that 20 gigs, and try and find something. It had an abundance of projects and work i had misplaced out of icloud, i don’t even know when. I don’t want it restored, i want it accessed and opened.

[Re-Titled by Moderator]