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Move most of the logic for extension action execution into the
ExtensionActionRunner (instead of the ExtensionActionAPI), which
eliminates some of the back-and-forth and makes a more common place
for execution logic and adds slightly finer-grained control for
what to execute. This also becomes more important with upcoming
changes for webRequest/document_start handling.

BUG=595087

Review URL: https://codereview.chromium.org/1804123003

Cr-Commit-Position: refs/heads/master@{#381603}