add to your functions.php or an included php file in your theme like helper functions or general

category-nice-name-body-class.php

<?php
//IMPORTANT: don't add above

add_filter( 'body_class', 'yourprefix_category_slug_body_class_single' );
/**
 * Add category body class to single posts any post type
 */
function yourprefix_category_slug_body_class_single( $classes ) {
	
	if ( is_single() ) :
		global $post;
		foreach( ( get_the_category( $post->ID)) as $category ) :
			$classes[] = 'category-'.$category->slug;
		endforeach;
	endif; //single post

	return $classes;
}