A hack to show the Set Featured Image modal when a meta box button is clicked.

index.js

wp.domReady( function () {
	var button = document.getElementById( 'mbwr-meta-box-button' );
	var container = document.getElementById( 'mbwr-meta-box-media-upload' );

	// NOTE: I'm not sure what timing issue this is avoiding, but it's necessary to avoid error.
	setTimeout( function () {
		wp.element.render(
			wp.element.createElement( wp.editor.PostFeaturedImage ),
			container
		);
	} );

	button.addEventListener( 'click', function () {
		var setterButton =
			container.querySelector( 'button.editor-post-featured-image__toggle' ) ||
			container.querySelector( 'button.editor-post-featured-image__preview' );

		if ( setterButton ) {
			setterButton.click();
		}
	} );
} );

index.php

<?php
/**
 * Plugin Name:     Meta Box With React
 * Plugin URI:      PLUGIN SITE HERE
 * Description:     PLUGIN DESCRIPTION HERE
 * Author:          YOUR NAME HERE
 * Author URI:      YOUR SITE HERE
 * Text Domain:     meta-box-with-react
 * Domain Path:     /languages
 * Version:         0.1.0
 *
 * @package         Meta_Box_With_React
 */

// Meta Box with React (mbwr)

function mbwr_enqueue_block_editor_assets() {
	wp_enqueue_script(
		'mbwr-meta-box-with-react',
		plugins_url( '/index.js', __FILE__ ),
		array( 'wp-dom-ready', 'wp-element', 'wp-editor' )
	);
}
add_action( 'enqueue_block_editor_assets', 'mbwr_enqueue_block_editor_assets' );

function mbwr_render_meta_box() {
	$title = __( 'Set featured image' );
?>
	<button id="mbwr-meta-box-button" type="button"><?php echo esc_html( $title ); ?></button>
	<!-- This is where we can create a hidden PostFeaturedImage component. -->
	<div id="mbwr-meta-box-media-upload" style="display: none;"></div>
<?php
}

function mbwr_add_meta_box( $post_type ) {
	if (
		use_block_editor_for_post_type( $post_type ) ||
		function_exists( 'gutenberg_can_edit_post_type' ) && gutenberg_can_edit_post_type( $post_type )
	) {
		add_meta_box(
			'mbwr-meta-box',
			__( 'Testing meta box' ),
			'mbwr_render_meta_box',
			null,
			'side'
		);
	}
}
add_action( 'add_meta_boxes', 'mbwr_add_meta_box', 10, 1 );