onetone Theme's Child Theme CSS vs. Custom CSS

All my css works fine when implementing via the “custom css” input field, which inserts the styles in the header of the pages. However, when I try to put the same css into my own child-theme style.css and enqueue it the same way I’ve enqueued for another wp site, nothing happens. Here’s my functions.php code:

<?php
// enqueue child theme css
add_action( 'wp_enqueue_scripts', 'my_child_theme_scripts' );
function my_child_theme_scripts() {
    wp_enqueue_style( 'style.css', get_template_directory_uri() . '/style.css' );
    wp_enqueue_style( 'style.scss', get_template_directory_uri() . '/style.css' );
}
?>

The site in question is used for my demo purposes and is at http://demoseer.com

What have I missed here? (And do you know if css entered in the “custom css” filed will remain intact after a theme update?)