Display posts with specific value first in query

If I understand it correctly, you would need to use the CASE operator in MySQL/MariaDB like so, to achieve that kind of sorting: (try a live demo on DB Fiddle)

ORDER BY (CASE
    # put posts with the specific meta value to the top
    WHEN (wp_postmeta.meta_value LIKE '%12345%') THEN 1

    # for the rest of posts, sort them by the meta value
    # use wp_postmeta.meta_value+0 if the value is number
    ELSE wp_postmeta.meta_value
END) ASC;

And WordPress or the WP_Meta_Query class doesn’t currently support such sorting, but you can use a custom query argument such as orderby_case and then use the posts_orderby filter to sort the posts:

1. Replace both the orderby and meta_query in your $args with this:

   'meta_query'     => array(
       // NOTE: The array key is necessary! Because we'll use that to get the
       //       alias that was used for this meta query clause.
       'customidexists' => array( // yes, you'd only need this one clause
           'key'     => 'custom_id',
           'compare' => 'EXISTS',
       )
   ),
   'orderby_case'   => 'customidexists', // must match the array key above
   

2. Add the CASE statement to the ORDER BY clause, using the posts_orderby filter:

   add_filter( 'posts_orderby', 'my_posts_orderby', 10, 2 );
   function my_posts_orderby( $orderby, $query ) {
       $clause_key = $query->get( 'orderby_case' );
       if ( 'customidexists' === $clause_key ) {
           $clauses = $query->meta_query->get_clauses();
   
           if ( isset( $clauses[ $clause_key ] ) ) {
               $alias = $clauses[ $clause_key ]['alias'];
               return "
                   (CASE
                       WHEN ($alias.meta_value LIKE '%12345%') THEN 1
                       # use $alias.meta_value+0 if the value is number
                       ELSE $alias.meta_value
                   END) ASC";
           }
       }
   
       return $orderby;
   }