Update Custom Post Type Meta Fields with the WordPress REST API

extend-rest-api.php

<?php
	register_meta('post', 'custom-field', [
			'object_subtype' => 'custom-post-type',
			'show_in_rest' => true
		]);

postman-request

/**
* https://stroopwafels.test/wp-json/wp/v2/design-template/
* Make sure to have something like https://github.com/WP-API/Basic-Auth active on your site
* Make the request with authentication (Basic Auth and username+password when using the link above)
*/

Send as body data (JSON):
{
	"title": "Test title",
	"meta": {
		"custom-field": "test"
	}
}

register-post-type.php

<?php
		register_post_type( 'custom-post-type', array(
			'label'        => __( 'Custom Post Type', 'textdomain' ),
			'show_ui'      => true,
			'menu_icon'    => 'dashicons-admin-customizer',
			'label'       => 'Custom Post Type'
			'supports'     => array( 'title', 'thumbnail', 'page-attributes', 'custom-fields' ),
			'public'       => false,
			'rewrite'      => false,
			'show_in_rest' => true,
		) );