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Record the timestamp when user request the extension for better UX on the
server side. The timestamp will be stored in the Pref as a
DictionaryValue with the format:
{ "$extension-id" : {"timestamp : "$java-time-as-string"}, }

The pref type is chagned from list to dict. It's safe to do so because the
only code path to set the value is behind a private API which is used by
no one now.

Also, allow ExtensionApiUnittest to pass TaskEnvironmentTraits to
BrowserWithTestWindowTest so that we can pause the clock for the test.


Bug: 1006899
Change-Id: I3c0463ed3847f6d14a14d31f6073355d6dc43716
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1940670
Commit-Queue: Owen Min <zmin@chromium.org>
Reviewed-by: Karan Bhatia <karandeepb@chromium.org>
Cr-Commit-Position: refs/heads/master@{#721624}