"The Backup tab displays any backup logs that have been created in UC Surface. The Backup tab allows you to create complete, time-stamped snapshots of your StudioLive. This can be especially useful when completing a project that may need to be revisited in the future. To create a backup, simply click on the Backup button. To restore any backup file, select it and click the Restore button."
This is what the manual says in section 5.7.3. "Backup Tab (StudioLive AI-series)". It is not explained, where the files are located (probably on computer running UC Surface). If there are backup files, they should be seen in the tab - and nowhere else. You may want to think about the word "backup" like it is described above, and what you want to acchieve.
Missing presets can only be restored by a firmware recovery, which simply is a new install of the firmware. It is important to use matching versions of firmware and software, which in your case are:
Universal Control 2.0 (Mac/PC) - 22.214.171.124902
UC Surface (iOS) - 126.96.36.199902
Capture (Mac/PC) 188.8.131.52943
RM Mixer Firmware v9244
AI Console Firmware v9194