How to add/edit advanced custom fields on custom post type’s WordPress REST API?

I have a custom post type called "notes" and also activated an Advanced Custom Field on that post type called "page_link". I want to add/edit the value of page_link using the REST API but I could not do it. I am only able edit native fields like title and the content. In my console, after success, noteLink is there but is equals to "null".

I have html like this:

<div class="mb-3">
  <label for="formInput1" class="form-label">Title</label>
  <input id="formInput1" class="new-note-title form-control" placeholder="Title">
</div>
<div class="mb-3">
  <label for="formTextarea1" class="form-label">Content</label>
  <textarea id="formTextarea1" name="" class="new-note-body form-control" placeholder="Content"></textarea>
</div>
<div class="mb-3">
  <label for="formInput2" class="form-label">Link</label>
  <input id="formInput2" class="new-note-link form-control" placeholder="Link">
</div>

javascript:

createNote(e) {

    var ourNewPost = {
        'title': $(".new-note-title").val(),
        'noteLink': $(".new-note-link").val(),
        'content': $(".new-note-body").val(),
        'status': 'publish'
    }

  $.ajax({
    beforeSend: xhr => {
      xhr.setRequestHeader("X-WP-Nonce", myData.nonce)
    },
    url: myData.root_url + "/wp-json/wp/v2/note/",
    type: "POST",
    data: ourNewPost,

    success: response => {
        //location.reload()
        console.log("Congrats")
        console.log(response)
    },
    error: response => {
      console.log("Sorry")
      console.log(response)
    }
  })
}

register post type like this:

function custom_post_types() {

    register_post_type('note', array(
      'capability_type' => 'note',
      'map_meta_cap' => true,
      'show_in_rest' => true,
      'supports' => array('title', 'editor', 'advanced-custom-fields'),
      'public' => false,
      'show_ui' => true,
      'labels' => array(
        'name' => 'Notes',
        'add_new_item' => 'Add New Note',
        'edit_item' => 'Edit Note',
        'all_items' => 'All Notes',
        'singular_name' => 'Note'
      ),
      'menu_icon' => 'dashicons-welcome-write-blog'
    ));
  }

register_rest_field on my functions.php like this:

function custom_rest(){

register_rest_field('note', 'noteLink', array(
  'get_callback' => function(){return get_field('page_link');}
));

}

add_action("rest_api_init", 'custom_rest');