GitLab

Removes another stateful component of LoginBubble to make it easier to
refactor in subsequent CLs.

Bug: 905512
Change-Id: If3dca30e9bb531ca1acb829e79db07be6f86d3d8
Reviewed-on: https://chromium-review.googlesource.com/c/1336969
Commit-Queue: Quan Nguyen <qnnguyen@chromium.org>
Reviewed-by: Jacob Dufault <jdufault@chromium.org>
Cr-Commit-Position: refs/heads/master@{#608484}