Not sure if I understand you correctly.
The files you see on the koboereader drive have nothing to do with the firmware version shown in the settings. The firmware is on the system partition that is not visible, and can not be backed up by default, through USB.
You can backup and restore your books, database (collections, reading progress, ...), configuration etc; you can not restore "firmware" other than downloading the appropriate firmware package from here and installing it (via .kobo/KoboRoot.tgz and .kobo/upgrade/).
If you were using mods that install themselves into the system partition you'll have to re-download and re-install them.
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