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This makes the AvatarToolbarButton toggle like a MenuButton similarly to
the adjacent BrowserAppMenuButton (which is actually a MenuButton).

Bug: chromium:849911
Change-Id: I30690c61dd9b9b58b80e28dcbc85dc9e72835b9d
Reviewed-on: https://chromium-review.googlesource.com/1091592
Commit-Queue: Peter Boström <pbos@chromium.org>
Reviewed-by: Bret Sepulveda <bsep@chromium.org>
Cr-Commit-Position: refs/heads/master@{#565440}