can’t access custom field in the meta json

hi

i have a custom post type book, and in its args i have

'show_in_rest'  => true,

now i want to add a custom field to it like so:

add_action( 'init', 'add_to_rest_test' );

function add_to_rest_test(){
   $meta_args = array(
      'type'         => 'string',
      'description'  => 'A meta key associated with a string meta value.',
      'single'       => true,
      'show_in_rest' => true,
   );
   register_post_meta( 'book', 'testing_field', $meta_args );
}

but then when i go to the post json: myexamplesite/wp-json/wp/v2/book…. there is no “meta” section. But if i change the code to regular post:

register_post_meta( 'post', 'testing_field', $meta_args );

in the json i do have a meta section:

"meta": {
    "testing_field": "",
    "footnotes": ""
  },

what am i missing here? appriciate any help