Create a new [wc_order] Contact Form 7 field tag which can only accept a valid WooCommerce order number.

cf7-woocommerce-order-field.php

<?php
/**
 * Plugin Name: Contact Form 7 WooCommerce Order Select Field
 * Description: Use the <code>[wc_order]</code> field in CF7 forms
 * Author: Pierre Saïkali
 * Author URI: https://saika.li
 * Text Domain: cf7wcp
 * Domain Path: /languages/
 * Version: 1.0.0
 */

namespace CF7_Woocommerce_Order_Field;

if ( ! defined( 'ABSPATH' ) ) {
	exit;
}

/**
 * Register the [wc_order] CF7 tag
 *
 * @return void
 */
function register_cf7_wc_order_tag() {
	wpcf7_add_form_tag(
		[ 'wc_order', 'wc_order*' ],
		__NAMESPACE__ . '\\output_cf7_wc_order_tag',
		[ 'name-attr' => true ]
	);
}
add_action( 'wpcf7_init', __NAMESPACE__ . '\\register_cf7_wc_order_tag', 10, 0 );

/**
 * Output the wc_order select field in a CF7 form
 *
 * @param object $tag
 * @return string HTML to output
 */
function output_cf7_wc_order_tag( $tag ) {
	if ( empty( $tag->name ) ) {
		return '';
	}

	$validation_error = wpcf7_get_validation_error( $tag->name );
	$class            = wpcf7_form_controls_class( $tag->type, 'wpcf7-wc_order' );
	$atts             = [];
	$value            = (string) reset( $tag->values );

	if ( $validation_error ) {
		$class .= ' wpcf7-not-valid';
	}

	$atts['type']          = 'text';
	$atts['name']          = $tag->name;
	$atts['class']         = $tag->get_class_option( $class );
	$atts['id']            = $tag->get_id_option();
	$atts['tabindex']      = $tag->get_option( 'tabindex', 'signed_int', true );
	$atts['autocomplete']  = $tag->get_option( 'autocomplete', '[-0-9a-zA-Z]+', true );
	$atts['aria-invalid']  = $validation_error ? 'true' : 'false';
	$atts['size']          = $tag->get_size_option( '10' );
	$atts['maxlength']     = $tag->get_maxlength_option();
	$atts['minlength']     = $tag->get_minlength_option();

	if ( $tag->has_option( 'readonly' ) ) {
		$atts['readonly'] = 'readonly';
	}

	if ( $tag->is_required() ) {
		$atts['aria-required'] = 'true';
	}

	if ( $tag->has_option( 'placeholder' ) || $tag->has_option( 'watermark' ) ) {
		$atts['placeholder'] = $value;
		$value               = '';
	}

	$value = $tag->get_default_option( $value );
	$value = wpcf7_get_hangover( $tag->name, $value );

	if ( isset( $_GET['wc_order' ] ) && ! empty( $_GET['wc_order' ]) ) {
		$value = (int) $_GET['wc_order' ];
	}

	$atts['value'] = $value;
	$atts          = wpcf7_format_atts( $atts );

	$html = sprintf(
		'<span class="wpcf7-form-control-wrap %1$s"><input %2$s />%3$s</span>',
		sanitize_html_class( $tag->name ),
		$atts,
		$validation_error
	);

	return $html;
}

/**
 * Handle the validation for our WooCommerce select input field
 *
 * @param object $result
 * @param object $tag
 * @return object
 */
function validate_wc_order_input_value( $result, $tag ) {
	$name = $tag->name;

	if ( $tag->basetype !== 'wc_order' ) {
		return $result;
	}

	$value = isset( $_POST[ $name ] ) ? trim( wp_unslash( strtr( (string) $_POST[$name], "\n", ' ' ) ) ) : '';
	$value = strtoupper( $value );

	// Check if value is empty?
	if ( $tag->is_required() && empty( $value ) ) {
		$result->invalidate( $tag, wpcf7_get_message( 'wc_order_field_required' ) );
	}

	// Check if we're dealing with a correct WooCommerce Order?
	if ( ! $order = wc_get_order( $value ) ) {
		$result->invalidate( $tag, wpcf7_get_message( 'wc_order_field_invalid' ) );
	}

	return $result;
}
add_filter( 'wpcf7_validate_wc_order', __NAMESPACE__ . '\\validate_wc_order_input_value', 10, 2 );
add_filter( 'wpcf7_validate_wc_order*', __NAMESPACE__ . '\\validate_wc_order_input_value', 10, 2 );

/**
 * Extend CF7 error messages to be customized
 *
 * @param array $messages
 * @return array
 */
function add_new_error_messages_for_wc_order_cf7_field( $messages ) {
	$messages = array_merge(
		$messages,
		[
			'wc_order_field_required' => [
				'description' => __( 'The order number is missing.', 'cf7wcp' ),
				'default'     => __( 'You need to provide your order number.', 'cf7wcp' ),
			],
			'wc_order_field_invalid' => [
				'description' => __( 'The selected order number is not valid.', 'cf7wcp' ),
				'default'     => __( 'Your order number is not valid.', 'cf7wcp' ),
			],
		]
	);

	return $messages;
}
add_filter( 'wpcf7_messages', __NAMESPACE__ . '\\add_new_error_messages_for_wc_order_cf7_field', 10, 1 );

/**
 * Everytime a CF7 form is sent with a [wc_order] field selected, 
 * add a note on the corresponding WC_Order to save the feedback on the order.
 * In my case, the order number field name is "your-order-number" and the user
 * feedback field name is "your-feedback".
 *
 * @return void
 */
function update_wc_order_meta_after_form_submission() {
	$submission = \WPCF7_Submission::get_instance();

	if ( ! $submission ) {
		return;
	}

	$posted_data = $submission->get_posted_data();
	$order_id    = (int) $posted_data['your-order-number'];
	$order       = wc_get_order( $order_id );
	$order->add_order_note( sanitize_textarea_field( $posted_data['your-feedback'] ) );
	$order->save();
}
add_action( 'wpcf7_mail_sent', __NAMESPACE__ . '\\update_wc_order_meta_after_form_submission' );
add_action( 'wpcf7_mail_failed', __NAMESPACE__ . '\\update_wc_order_meta_after_form_submission' );

Full tutorial:

Tutorial (in French) available at https://mosaika.fr/creation-champ-formulaire-cf7/

End result: