register_post_meta.php

<?php 

register_post_meta( 'page', 'sidebar_plugin_meta_block_field', [
    'show_in_rest'      => [
				'prepare_callback' => __NAMESPACE__ . '\\prevent_meta_exposition'
			],
    'single'            => true,
    'type'              => 'string',
    'sanitize_callback' => 'sanitize_text_field',
] );

/**
 * Keep a meta key private in the REST API, only to users that can edit the current post.
 *
 * @param mixed $value
 * @param \WP_REST_Request $request
 *
 * @return string
 */
function prevent_meta_exposition( $value, $request ) {
	if ( ! current_user_can( 'edit_post', $request->get_param( 'id' ) ) ) {
		return '';
	}

	return $value;
}