Move source of truth for SetPreferredDataTypes to SyncUserSettings

This is a followup to https://crrev.com/c/1382483 which did the same
for the getters.

Bug: 884159
Change-Id: I86e5f98434e20f3ff660065f3d8873e2e2e5e81c
Reviewed-on: https://chromium-review.googlesource.com/c/1403131
Reviewed-by: Mohamed Amir Yosef <mamir@chromium.org>
Commit-Queue: Marc Treib <treib@chromium.org>
Cr-Commit-Position: refs/heads/master@{#622423}
8 files changed