Error [Column ‘post_title’ cannot be null] when title is disabled for Custom post type

I would suggest the following improvements for better code readability and to make it easier to maintain later.

1. Assuming you’ve removed title from your custom post type using the following function :

   remove_post_type_support( 'slider', 'title' )
   

   Now if you use name="post_title" instead of name="wys_slider_title"
   WordPress will still use it and update the post title accordingly. Hence you don’t have to worry about the title and you can focus on your custom fields. This results in a much better code and solves your problem of duplicating the title and then saving it.
   *This helps you avoid using wp_insert_post_data additional filter.
   *And since you’re not manually updating the title using wp_update_post function, you don’t have to worry about the save_post infinite loop.

2. Before you save any data, you want to make sure there’s nothing malicious in there. Fortunately, WordPress provides a bunch of functions for Data Validation

   // Use:
   update_post_meta( $post_id, 'my_meta_box_text', wp_kses( $_POST['my_meta_box_text'], $allowed ) );
   // Instead of:
   update_post_meta( $post_id, 'my_meta_box_text', $_POST['my_meta_box_text'] );
   

3. Use save_post_{$post_type} instead of plain save_post, This helps you avoid unnecesary IF statements
   e.g. In your case,
   add_action( 'save_post_slider', 'wys_slides_save_details' );

   you won’t need to wrap your logic around an IF statement

   if( $post_type == 'slider' ) {...CODE...}
   

   Since save_post_slider will only run for Slider post type.