Sort order of next/prev sibling page

I think in this case it is probably easiest to create your own function or two. I’m giving you a rough outline on how to do it below.

// use the same filter to get the same results
add_filter( 'posts_fields', 'wpcf_create_temp_column' );
add_filter( 'posts_orderby', 'wpcf_sort_by_temp_column' );
// perform query
$q = new WP_Query( [ 
  'post_type' => 'pages', 
  'fields' => 'ids', 
  'posts_per_page' => -1 
] );
remove_filter( 'posts_fields','wpcf_create_temp_column' );
remove_filter( 'posts_orderby', 'wpcf_sort_by_temp_column' );

// array of ids
$a = $q->posts;

// index of current post
$i = array_search( get_the_ID(), $a );

// id of previous post
$pp_id = $a[ $i - 1 ];
// with the id get the permalink or whatever you need
$pp_pl = get_the_permalink( $pp_id );

// id of next post
$np_id = $a[ $i + 1 ];
// with the id get the title or whatever you need
$np_ti = esc_html( get_the_title( $np_id ) );