Decouple the browsing data counters initialization and start.

Previously, the counters started counting immediately after the initialization, which is called during the initialization of ClearBrowserDataHandler, and that happens immediately when chrome://settings is opened.
On the other hand, there was no trigger when the ClearBrowserDataHandler page was initialized, i.e. when chrome://settings/clearBrowserData opened.

This had two adverse effects:

- Counters started counting too soon (which is unnecessary as the user might have opened chrome://settings for any other reason)
- Reloading chrome://settings/clearBrowserData did not trigger counter restart

BUG=510028

Review URL: https://codereview.chromium.org/1342093003

Cr-Commit-Position: refs/heads/master@{#349112}
5 files changed