Prerequisite: you must switch on the Bottom box option (under Slide-out TOC > Slide-out custom content boxes)
Add custom content at the bottom of the slide-out panel.
The container’s selector of the custom content is .wpj-jtoc--slide-out-custom-box-bottom
add_action( 'joli_toc_slide_out_box_bottom', function (){
echo do_shortcode('[my-shortcode]);
});