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Hash dance timer usually starts off whenever the
AutoEnrollmentCientImpl is going to start
i.e. AutoEnrollmentCientImpl::Start(). However,
as PSM is being executed in the beginning,
before Hash dance sequentially, that will make the
resulting Hash timer record Hash dance duration +
PSM duration.

This CL is starting the timer of Hash dance only when
preparing and sending off the Hash dance request. Also,
it adds its required regression tests.

BUG=chromium:1157317

Change-Id: Ie4aa0b8a3bd6cf296e3804995cacc45c23833c80
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2582121
Commit-Queue: Amr Aboelkher <amraboelkher@google.com>
Reviewed-by: Pavol Marko <pmarko@chromium.org>
Reviewed-by: Maksim Ivanov <emaxx@chromium.org>
Reviewed-by: Roland Bock <rbock@google.com>
Cr-Commit-Position: refs/heads/master@{#835850}