Revert "Move Settings backup and restore metric logging from SettingsProvider to SettingsHelper"

This reverts commit 355f9bac.

Reason for revert: Likely culprit for b/384668761  - verifying through ABTD before revert submission. This is part of the standard investigation process, and does not mean your CL will be reverted.

Change-Id: Ic5d6681c59214ef0c3f79cbf775e0d2b9d6d2669