How can a default site icon be set in customizer?

From my research there are only two questions I’ve found around this topic on this site:

• How to change in customizer the “site identity” tab required capabilities
• how to change default icon of custom plugin?

outside of the site I did find:

• How to Add a Default Site Icon in Theme’s Customizer

but when I try:

function default_icon() {
  global $wp_customize;
  $wp_customize->get_setting('site_icon',array (
    'default' => home_url() . 'img/test.png'
  ));
}
add_action('customize_register','default_icon');

I’ve also tried add_setting with:

function default_icon() {
  global $wp_customize;
  $wp_customize->add_setting('site_icon', array(
    'default' => home_url() . 'img/test.png'
));
}
add_action('customize_register','default_icon');

but that doesn’t work either. It will not show the default icon in the drag and drop area and renders “No Image selected”:

In my functions.php how can I code my theme to render the default icon presently being used in the drag and drop area?

After further testing I can set the default when I code:

add_action('customize_register','default_icon',10,2);

and I can see it in a dump of $wp_customize but as far as rendering it will not.