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- Add the callback invoked after the observers.
- Flush the pending change in pref.

This will let WebView consistently see the persisted metrics after
restart.

Bug: 1076549
Change-Id: I9ab7a228bfd0431ead9545c37a07905c1a41ec8e
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2226067
Commit-Queue: Tao Bai <michaelbai@chromium.org>
Reviewed-by: Bo <boliu@chromium.org>
Cr-Commit-Position: refs/heads/master@{#776150}