[Autofill Assistant] Move header delegate into native side.

Change-Id: I9e66727766422a18bc4e4c5618c49e332c548087
Reviewed-on: https://chromium-review.googlesource.com/c/1426685
Commit-Queue: Jordan Demeulenaere <jdemeulenaere@chromium.org>
Reviewed-by: Stephane Zermatten <szermatt@chromium.org>
Cr-Commit-Position: refs/heads/master@{#625152}
18 files changed