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This moves the core functionality (frontend, backend and local storage
implementations) to src/extensions while leaving Chrome-specific sync storage
and managed storage implementations in src/chrome.

BUG=348058
TEST=unit_tests *Storage*:*Settings* browser_tests ExtensionSettings*
TBR=zea@chromium.org for header file move touching chrome/browser/sync/test/integration/extension_settings_helper.cc

Review URL: https://codereview.chromium.org/189263013

git-svn-id: svn://svn.chromium.org/chrome/trunk/src@255901 0039d316-1c4b-4281-b951-d872f2087c98