WordPress Customizer Not Setting Custom Settings or Controls

The section you created 'Social Media Icons' doesn’t show because is empty it doesn’t have any control, this is because you didn’t set the correct ID in the control arguments, it should be like this in socialcustomizersection.php:

// control
$wp_customize->add_control( $social_site, array(
    'type'     => 'url',
    'label'    => $label,
    'section'  => 'ct_alter_social_array_filter', //it should be the ID you Set for the section
    'priority' => $priority
) );

also in footer.php you are loading outputicons.php and that only contains a function, you need to call the function, put this after the require_once on the footer.php or at the end of outputicons.php:

my_social_icons_output();

the section will show, i added 2 here for testing the output:

and they work: