You will need to use the ID value returned by $category[0]->category_parent and pass it through get_term()
$category = get_the_category();
$category_parent_id = $category[0]->category_parent;
if ( $category_parent_id != 0 ) {
$category_parent = get_term( $category_parent_id, 'category' );
$css_slug = $category_parent->slug;
} else {
$css_slug = $category[0]->slug;
}
//ref:https://wordpress.stackexchange.com/users/8054/rachel-baker
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