Changing default admin column sorting to an ACF Date Picker field

it looks like the problem is caused by the “Post Types Order” plugin I
have installed

Yes, I believe so because your code actually worked for me, but after I installed and activated the plugin, your code no longer worked as expected.

I have it set to not order news post types, but for some reason it’s
still adding its sorting to the main query.

I don’t know how you set it, but try one of these:

1. Set ignore_custom_sort (it’s a custom WP_Query parameter) to true like so:

   switch ( $order_by ) {
       case 'news-date':
           $query->set( 'meta_key', 'date' );
           $query->set( 'orderby', 'meta_value_num' );
           $query->set( 'ignore_custom_sort', true );
           break;
   }
   

2. Or you can also use the pto/posts_orderby/ignore hook to disable the plugin’s sorting:

   add_filter( 'pto/posts_orderby/ignore', function( $ignore, $order_by, $query ){
       if ( 'lesson' === $query->get( 'post_type' ) ) {
           $ignore = true;
       }
       return $ignore;
   }, 10, 3 );