Move usage of BackendUserSettingsDataProvider to the new Storage.js

Resolves: #66868
Releases: master
Change-Id: Ibc6d57368ca8ebc8b4e5e026cbaaa5d80d428d1c
Reviewed-on: http://review.typo3.org/39311


Reviewed-by: Benjamin Mack <benni@typo3.org>
Tested-by: Benjamin Mack <benni@typo3.org>
Reviewed-by: Andreas Fernandez <typo3@scripting-base.de>
Tested-by: Andreas Fernandez <typo3@scripting-base.de>