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The logic to execute a task on a timer, persisted across Chrome
restarts, already existed in account_fetcher_service.
This CL extracts it in a new class, and reuses it in ProfileInfoCache.

The metric is not loaded exactly at the same time it was before:
it used to be logged for each profile, but now it's logged per Chrome
run. This makes more sense given the nature of the metric.

Fixed: 1060096
Change-Id: I5b8c709f088709934b8ad54fa9a46fac091923cf
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2096743
Commit-Queue: David Roger <droger@chromium.org>
Reviewed-by: Monica Basta <msalama@chromium.org>
Cr-Commit-Position: refs/heads/master@{#749621}