Translate are not working for standard admin

The only instance of "Count" I can see in the default domain’s admin file has a context value of "Number/count of items". So your code should be:

add_action( 'admin_init', 'action_admin_init' );
function action_admin_init() {
  _ex( 'Count', 'Number/count of items' );
}

Ref: _ex.