wp_get_post_terms is difference obj model than the one in rest api response

I’m building a mobile app and using the rest API on WordPress to do that, I am customizing the /wp/v2/posts response by using the following code:

add_filter('rest_prepare_post', 'custome_posts_response', 10, 3);

function custome_posts_response($data, $post, $context)
{
    $newspapers = wp_get_post_terms($post->ID, 'newspaper');
    $categories = wp_get_post_terms($post->ID, 'category');
    $tags = wp_get_post_terms($post->ID, 'post_tag');

    return [
        "id" => $post->ID,
        "title" => $post->post_title,
        "format" => $data->data['format'],
        "date" => $data->data['date'],
        "slug" => $data->data['slug'],
        "status" => $data->data['status'],
        "externalFeaturedImage" => $data->data['external_featured_image'],
        "sourceLink" => $data->data['source_link'],
        "content" => $post->post_content,
        "excerpt" => $post->post_excerpt,
        "author" => $data->data['author'],
        "newspaper" => $newspapers,
        "categories" => $categories,
        "tags" => $tags,
        "commentCount" => $post->comment_count,
        "commentStatus" => $post->comment_status
    ];
}

My problem is the term OBJ in my above code print like that:

{
  term_id: 4,
  name: "Arabs Turbo",
  slug: "arabs-turbo",
  taxonomy: "newspaper",
  description: "",
  parent: 0,
  count: 181,
  filter: "raw"
}

I guess that because it a query for selecting all fields directly from the database and I don’t wanna that,

I need the response to be exactly as WP REST API Term model like the following:

{
   "id": 9,
   "count": 27,
   "description": "",
   "link": "http://localhost/carstime/newspapers/ahmed-el-wakil/",
   "name": "Ahmed El Wakil",
   "slug": "ahmed-el-wakil",
   "taxonomy": "newspaper",
   "meta": [],
   "_links": //...
}

So what method/function should I use to accomplish this instead of using wp_get_post_terms or mapping though the array using array_map for every taxonomy.

function custome_posts_response(WP_REST_Response $data, WP_POST $post, WP_REST_Request $request)
{
    $newspapers = wp_get_post_terms($post->ID, 'newspaper');
    $categories = wp_get_post_terms($post->ID, 'category');
    $tags = wp_get_post_terms($post->ID, 'post_tag');

    $newspaper_ctrl = new WP_REST_Terms_Controller('newspaper');
    $category_ctrl = new WP_REST_Terms_Controller('category');
    $tags_ctrl = new WP_REST_Terms_Controller('post_tag');

    $newspapers = array_map(function( WP_TERM $newspaper ) use ($newspaper_ctrl, $request) {
        return $newspaper_ctrl->prepare_item_for_response($newspaper, $request)->data;
    }, $newspapers);

    $categories = array_map(function( WP_TERM $category ) use ($category_ctrl, $request) {
        return $category_ctrl->prepare_item_for_response($category, $request)->data;
    }, $categories);

    $tags = array_map(function( WP_TERM $tag ) use ($tags_ctrl, $request) {
        return $tags_ctrl->prepare_item_for_response($tag, $request)->data;
    }, $tags);

    return [
        "id" => $post->ID,
        "title" => $post->post_title,
        "format" => $data->data['format'],
        "date" => $data->data['date'],
        "slug" => $data->data['slug'],
        "status" => $data->data['status'],
        "externalFeaturedImage" => $data->data['external_featured_image'],
        "sourceLink" => $data->data['source_link'],
        "content" => $post->post_content,
        "excerpt" => $post->post_excerpt,
        "author" => $data->data['author'],
        "newspaper" => $newspapers,
        "categories" => $categories,
        "tags" => $tags,
        "commentCount" => $post->comment_count,
        "commentStatus" => $post->comment_status
    ];
}