Adding custom meta boxes to specified custom post type

The fourth parameter is $screen, which in your case is set to post, so all you have to do is specify the website post type instead:

function website_add_meta_box() {
    add_meta_box(
        'website-website',
        __('Website', 'website'),
        'website_html',
        'website',
        'normal',
        'default'
    );
}

Documentation here: https://developer.wordpress.org/reference/functions/add_meta_box/

As an aside, your save_post hook applies to any post or custom post type being saved, but if website_website_url and website_website_source_code only apply to the website post type, you can add an additional check:

function website_save($post_id) {
    if (defined('DOING_AUTOSAVE') && DOING_AUTOSAVE) return;
    if (!isset($_POST['website_nonce']) || !wp_verify_nonce($_POST['website_nonce'], '_website_nonce' )) return;
    if (!current_user_can('edit_post', $post_id)) return;
    if (get_post_type($post_id) !== 'website') return;

    if (isset($_POST['website_website_url']))
        update_post_meta($post_id, 'website_website_url', esc_attr($_POST['website_website_url']));
    if (isset($_POST['website_website_source_code']))
        update_post_meta($post_id, 'website_website_source_code', esc_attr($_POST['website_website_source_code']));
}

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