Use a supplemental engine when searching WooCommerce Orders. See https://searchwp.com/docs/kb/searching-woocommerce-orders/

functions.php

<?php

/**
 * When performing an admin search for WooCommerce Orders, use the 'Orders' SearchWP engine
 */
function my_searchwp_search_args( $args ) {
	$search_in_admin = apply_filters( 'searchwp_in_admin', false );

	if ( wp_doing_ajax() || empty( $_GET['post_type'] ) || ! is_admin() || empty( $search_in_admin ) ) {
		return $args;
	}

	if ( 'shop_order' !== $_GET['post_type'] ) {
		return $args;
	}

	// WooCommerce adds some limiting that we're going to get rid of here
	add_filter( 'searchwp_include', function( $ids ){
		return is_admin() && is_search() ? array() : $ids;
	}, 999 );

	$args['engine'] = 'orders';

	return $args;
}

add_filter( 'searchwp_search_args', 'my_searchwp_search_args' );