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Classes derived from printing::PrintManager each process a similar set
of messages, such as DidPrintDocument, GetDefaultPrintSettings, and
ScriptedPrint.  The framework necessary for handling these is very
similar across the classes, even if some of the classes need to do
something different for some particular message.

Simplify the code by pushing this common framework into the base class
printing::PrintManager.

Broken out of work to resolve a printing issue when print preview is
disabled in [1].

[1] https://crrev.com/c/1700275

Bug: 974480
Change-Id: If5a6a2f100900d9261f7c396f6bec55f299fea3c
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1714807Reviewed-by: Tao Bai <michaelbai@chromium.org>
Reviewed-by: Andrey Kosyakov <caseq@chromium.org>
Reviewed-by: Lei Zhang <thestig@chromium.org>
Commit-Queue: Lei Zhang <thestig@chromium.org>
Cr-Commit-Position: refs/heads/master@{#683009}