Get theme color palette from the active WordPress Theme (WP REST API)

crofte-admin.js

;( function( $, window, document, undefined ) {
  
	// Prepare the async function
	async function fetchColorsJSON() {
		const response = await fetch(crofte.rest_theme_url, {
			"headers": {
				"Accept": "application/json, */*;q=0.1", // optional
				"X-WP-Nonce": crofte.rest_nonce,
				"Sec-Fetch-Mode": "cors",                // optional
				"Sec-Fetch-Site": "same-origin"          // optional
			},
			"method": "GET", // optional
			"mode": "cors"   // optional
		});
		const ActiveTheme = await response.json();
    
		// Control what you need to control here, ActiveTheme might not be an array.
		return ActiveTheme[0].theme_supports['editor-color-palette'];
	}
  
	// Use the async function
	fetchColorsJSON().then(colors => {
		if ( Array.isArray( colors ) ) {
			// We should have a table of Object reprenseting the colors.
			console.log( colors );
		} else {
			// If you don't, prepare a fallback.
		}
	});
} )( jQuery, window, document );

enqueue.php

<?php 
/**
 * Enqueue script files to use WP REST API
 *
 * @since  1.0
 * @author Geoffrey Crofte
 */
function crofte_enqueues() {
	global $pagenow;

	if ( $pagenow === 'A PAGE WHERE YOU USE THIS SCRIPT' ) {
		wp_enqueue_script( 'crofte-main', plugin_dir_url( __FILE__ ) . 'assets/js/crofte-admin.js', array( 'jquery' ), '1.0.0', true );

		$crofte_datas = array(
			'rest_nonce' => wp_create_nonce( 'wp_rest' ),
			'rest_theme_url' => esc_url_raw( rest_url() ) . 'wp/v2/themes?status=active',
		);
		wp_localize_script( 'crofte-main', 'crofte', $crofte_datas );
	}
}
add_action( 'admin_enqueue_scripts', 'crofte_enqueues' );

Answering my own question on Twitter.
If you have a solution full PHP, I take it with joy.

https://twitter.com/geoffreycrofte/status/1538246202721984512