Custom UL classes and disable menu box in pages/posts

There are a number of plugins which allow you to show widgets on particular sections. Here are a couple examples (I am in no way affiliated with these other plugins and can not guarantee their functionality):

https://wordpress.org/plugins/restrict-widgets/
https://wordpress.org/plugins/widget-options/

Otherwise if you would like to do this programmatically, you may update the previously sent filters to:

add_filter( 'advanced-sidebar-menu/menus/category/is-displayed', '__return_true' );
add_filter( 'advanced_sidebar_menu_category_ids', 'include_all_parent_terms', 1, 4 );
function include_all_parent_terms( $term_ids, $args, $instance, $object ) {
if ( 'category' !== $object->get_taxonomy() ) {
return $term_ids;
}

//ADD CATEGORIES YOU WANT TO DISPLAY TO THIS ARRAY
$categories = array( 'news' );

if( is_page( 29 ) || is_category( $categories ) ) {
return get_terms( array(
'parent' => 0,
'fields' => 'ids',
'taxonomy' => 'category',
'hide_empty' => true,
) );
}

return array();
}

This will display the widget on your blog page and whatever categories you add to the $categories array, marked with.
//ADD CATEGORIES YOU WANT TO DISPLAY TO THIS ARRAY

It appears you are using an “Advanced Menu” widget on the page. I am unfamiliar with that widget but I took a quick look anyway. I have confirmed that it is added to that sidebar and the options appear to be correct.

Due to my lack of knowledge of this widget, I am unable to provide a solution. I recommend reaching out to the developer of the widget to see if they have a solution.