Archive page for WordPress Custom Post Type doesn’t show pagination from paginate_links()

I have a custom post type with courses-events as the slug.

In functions.php, I have:

add_action( 'pre_get_posts', 'custom_archive_items' );
function custom_archive_items( $query ) {
  if ($query->is_main_query() && !is_admin() && is_post_type_archive( 'courses-events')) {
    $query->set( 'posts_per_page', '1' );
  }
}

I know the above is firing for my archive page if I dump $query in the condition, it is visible.

On archive-courses-events.php I have simply:

if ( have_posts() ) :
  while(have_posts()) : the_post();
    <!-- my output -->
  endwhile;
  
  echo paginate_links();
endif;

I have 2 posts and as posts_per_page is set to 1, but 2 posts appear and I do not see pagination.

I don’t understand why this isn’t working as everything I’ve read says that this is the minimum necessary for this to work?