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This is a reland of fa8de986

Original change's description:
> [Profile picker] Use system profile on startup when showing the picker
>
> This CL changes the logic to load the startup profile whenever the
> profile picker should be loaded. It instead loads the guest profile
> to indicate the picker should be open. This speeds up showing the picker
> when the last profile used is heavy to load. The CL also unifies the
> logic to decide whether to show the new picker (or the old user manager)
> into one function, GetStartupProfile().
>
> There is one behavioral difference: the new code directly opens browser
> windows if the user had multiple profiles open last time. This is desired
> because having multiple profiles open simultaneously the last time is a
> strong signal the user wants to continue this way. Note that having
> multiple profiles open the last time happens only in limited situations,
> e.g. via chrome://restart or via session restore (when logging out /
> switching off the machine with multiple profiles' windows open).
>
> Bug: 1150330
> Change-Id: Iae9744f44bc242e9aaaf8f287cc29e1089326786
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2532460
> Commit-Queue: Jan Krcal <jkrcal@chromium.org>
> Reviewed-by: David Roger <droger@chromium.org>
> Cr-Commit-Position: refs/heads/master@{#828665}

Bug: 1150330
Change-Id: I457871e2041eb09eb90fb31f773d095b47aeb462
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2547040
Commit-Queue: Jan Krcal <jkrcal@chromium.org>
Reviewed-by: Avi Drissman <avi@chromium.org>
Reviewed-by: Tommy Martino <tmartino@chromium.org>
Reviewed-by: David Roger <droger@chromium.org>
Cr-Commit-Position: refs/heads/master@{#837191}