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The main goal of the CL is to separate the desktop-specific HTML from
the shared HTML to make testing more straightforward.

Since this was already a refactoring CL, I also applied the fixes
surfaced by the presubmit checks.

Bug: 952034
Change-Id: I963dff8ef49ef3b78b585aa2040876953a2de004
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1925688
Commit-Queue: Aran Gilman <gilmanmh@google.com>
Reviewed-by: Wei-Yin Chen (陳威尹) <wychen@chromium.org>
Cr-Commit-Position: refs/heads/master@{#717963}