Add my new post type to WordPress category and tag archives

That is actually the exact same solution. WordPress Core specifically limits Category and Tag Archives (and widgets, etc.) to only be displayed for the ‘post’ post-type. The only way around this is to add other post-types to the pre_get_posts filter which is what that linked code is doing.

This line specifically:

// Replace these slugs with the post types you want to include.
		$cptui_post_types = array( 'my_post_type', 'my_other_post_type' );

Is used to create an array of post types that you want to be added to the pre_get_post filter for Categories and Tags. In your case, you’d change it to:

// Replace these slugs with the post types you want to include.
		$cptui_post_types = array( 'movies', 'books' );

Hope that’s helpful!
Jim

You don’t have to be an expert coder; these go in the functions.php file of your child theme.

If you’re very uncomfortable with coding, this plugin should do what you need:
https://wordpress.org/plugins/custom-post-type-taxonomy-archives/