Turns out my PHP skills are not exactly top notch. Which is something I’m ok with. ??
Upon further investigation of the source code, I figured out how you can access the three options from the Featured Content section of the Customizer. You need to use an array:
$featured = (array) get_option( 'featured-content' );
if ( has_tag( $featured['tag-name'] ) ) echo 'This is a featured post';
Hope this helps someone!