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() {
      plugin_dir_url( __FILE__ ) . 'js/plugin.js',

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