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In preparation for adding webui message handlers, it will be cleaner to have the dialog-related code in a separate file.

Change-Id: I926788149d63a512055d1bb1932f60362f6b6172
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2626811Reviewed-by: John Palmer <jopalmer@chromium.org>
Reviewed-by: Satoru Takabayashi <satorux@chromium.org>
Reviewed-by: Keith Lee <keithlee@chromium.org>
Commit-Queue: Kenton Lam <kentonlam@google.com>
Cr-Commit-Position: refs/heads/master@{#843384}