GitLab

Use the WidgetBase implementations instead of going via the
WebWidgetClient.

BUG=1097816

Change-Id: Ib08b5748806fe3862ac291d354043326d3172282
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2419129Reviewed-by: danakj <danakj@chromium.org>
Commit-Queue: Dave Tapuska <dtapuska@chromium.org>
Cr-Commit-Position: refs/heads/master@{#809421}