Reduce RenderSearchField dependency from SearchInputType.

Move updateCancelButtonVisibility from RenderSearchField to
SearchInputType, and simplify the implementation.

The updateCancelButtonVisibility call in updateFromElement is moved to
SearchInputType::updateInnerTextValue, which is called for every value
changes not by a user.

BUG=274205
TEST=none; should have no behavior changes.

Review URL: https://chromiumcodereview.appspot.com/23030003

git-svn-id: svn://svn.chromium.org/blink/trunk@156276 bbb929c8-8fbe-4397-9dbb-9b2b20218538