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Delete or replace with the appropriate base/ headers. Fix a few lint
errors and do IWYU along the way.

Change-Id: If2066861079a6b7c82d5431b03f2da1db0b7159b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1775447Reviewed-by: Chris Palmer <palmer@chromium.org>
Reviewed-by: Kentaro Hara <haraken@chromium.org>
Reviewed-by: Ken Rockot <rockot@google.com>
Commit-Queue: Lei Zhang <thestig@chromium.org>
Cr-Commit-Position: refs/heads/master@{#691961}