How to fetch category name in web story custom api

Hello Team,

We are using a web story plugin and created a custom rest API and fetched all web stories from this custom API.

Please find the below function what we are used :

// displayed all webstories using api

add_action( 'rest_api_init', 'get_all_webstory_posts' );   

function get_all_webstory_posts() {
    register_rest_route( 'wp/v2', '/web-story-list', array(
        'methods' => 'GET',
        'callback' => 'get_all_webstories_callback'
    ));
}

function get_all_webstories_callback( $request ) {
    // Initialize the array that will receive the posts' data. 
    $posts_data = array();
    // Receive and set the page parameter from the $request for pagination purposes
    $paged = $request->get_param( 'page' );
    $paged = ( isset( $paged ) || ! ( empty( $paged ) ) ) ? $paged : 1; 
    // Get the posts using the 'post' and 'news' post types
    $posts = get_posts( array(
            'paged' => $paged,
            'posts_per_page' => -1,            
            'post_type' => array( 'web-story' ),
        )
    ); 
    // Loop through the posts and push the desired data to the array we've initialized earlier in the form of an object
    foreach( $posts as $post ) {
        $id = $post->ID; 
        $post_thumbnail = ( has_post_thumbnail( $id ) ) ? get_the_post_thumbnail_url( $id ) : null;

        $posts_data[] = (object) array( 
            'id' => $id, 
            'slug' => $post->post_name, 
            'type' => $post->post_type,
            'title' => $post->post_title,
            'featured_img_src' => $post_thumbnail,
			'permalink' => get_permalink( $id ),
            'published_date' => get_the_time('M d,Y', $id),
             'cat' => get_categories(),
			
        );
    }                  
    return $posts_data;                  
}

In above mentioned code we got result id,slug,title,featured_img_src, and published date but we don’t get category name.

So our query is :
1. We have categories and this category assigned some posts also we are trying to fetch category names on our API it’s not getting. Can You please guide us on how to fetch categories names on API.
3. Is there any different name on fetching categories EX: web_story_category

Please let me know how to fetch categories name on API

Thank You