Integrate new tabstrip animations with DoLayout.

The new animation system is used to handle layout that happens while
no animations are running (e.g. when resizing the strip).

Bug: 958173
Change-Id: I53c547f4ff9139f549a26e636748f9a5c3086101
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1623134
Commit-Queue: Taylor Bergquist <tbergquist@chromium.org>
Reviewed-by: Bret Sepulveda <bsep@chromium.org>
Cr-Commit-Position: refs/heads/master@{#663323}