Register meta field to show in Rest API

register-meta-field.php

add_action( 'init', function() {

	// replace your-post-type-slug and your-meta-field-name with your actual data
	register_post_meta( 'your-post-type-slug', 'your-meta-field-name', array(
		'single'         => true,
		'type'           => 'string',
		'default'        => '',
		'auth_callback'  => '__return_true',
		'show_in_rest'   => true,
	) );

}, 99 );