What is the standard way to use the version of React that ships with Gutenberg on the front end?

I found it, wp-element. The @wordpress/scripts should handle the heavy lifting of transforming the JSX in the proper way.

add_action( 'wp_enqueue_scripts', 'my_enqueue_plugin_js' ); // Loads on frontend

function my_enqueue_plugin_js() {
    wp_enqueue_script(
      'my-plugin-frontend',
      plugin_dir_url( __FILE__ ) . 'js/plugin.js',
      ['wp-element']
    );
}

Once we do this we will have window.wp.element available in our JavaScript. This contains the ReactDOM render() function as well as createElement() if you wanted to write React without JSX.

— How to Enqueue React in A WordPress Theme or Plugin