Can a directory be added to a WordPress post slug with a function?

I want to add a /news/ before every post slug. Like this:

example.com /news/ post-slug/

If I add the /news/ in the permalinks settings, every custom post type is broken after it.

I tried to add the following to every register_post_type:

    'with_front'        => false,

But that doesn’t help.

I also tried the code from here:

$post_type = <POST TYPE NAME> # Define your own as a string
$new_slug = <WANTED SLUG> # Define your own as a string

add_filter( 'register_post_type_args', function($args, $post_type){
  if ( 'post_type' == $post_type )
     $args['rewrite'] = array( 'slug' => $new_slug );

  return $args;

}, 10, 2 );

Unfortunately that doesn’t work either.

Is there any way to add the /news/ without breaking the other post types?

Here’s the current code for my custom post type:

add_action( 'init', 'cpt_custom' );
function cpt_custom() {
    register_post_type( 'custom',
        array(
        'rewrite'           => array( 'slug' => 'custom' ),
        'hierarchical'      => true,
        'public'            => true,
        'has_archive'       => true,
        'show_in_rest'      => true,
        'with_front'        => true,
        )
    );
}

In the permalink settings it’s set to /news/%postname%/