How can I use Woocommerce $product->get_attribute in functions.php? (if at all)

get_attribute() is a method of the WC_Product object, so $product needs to be an instance of WC_Product that represents the current product. Your code on its own won’t work because $product is likely not defined.

So you need to define $product, but you also need to determine which product it should be defined as. In your case it needs to be the current product when viewing a single product page. You can do this by:

1. Determining if you’re on a single product page.
2. If you are, get a WC_Product instance of the product that the page is for.

For #1, use is_product(), and for #2 use get_queried_object() to get a post object for that product, combined with wc_get_product() to get the WC_Product object for that product.

Altogether that looks like this:

add_action(
    'wp_enqueue_scripts',
    function() {
        if ( function_exists( 'is_product' ) && is_product() ) {
            $post    = get_queried_object();
            $product = wc_get_product( $post );

            if ( 'vertical' === $product->get_attribute( 'pa_orientation' ) ) {
                // Enqueue your stylesheet.
            }
        }
    }
);

Note that I added a check for function_exists( 'is_product' ). The is_product() function is a WooCommerce function, so your site would crash if WooCommerce was deactivated. Checking for the function before using it prevents that.