Move api_resource{,manager} out of src/chrome

This is a mechanical change. No new DEPS are
introduced into src/extensions.

clang_format was also applied to all touched
extensions code, for great justice.

BUG=349930
TBR=wez@chromium.org,yoz@chromium.org,rpaquay@chromium.org,erg@chromium.org for mechanical changes

Review URL: https://codereview.chromium.org/182213005

git-svn-id: svn://svn.chromium.org/chrome/trunk/src@255575 0039d316-1c4b-4281-b951-d872f2087c98
SVN changes up to revision 255575