How to import featured image using WP Rest API from another WP installation

This endpoint /wp/v2/posts does not return featured image src url. It provides featured image id, that you can use to get image url by performing another REST request. Following function performs a rest request using media id and get image src url.

/**
 * Get media url from WP REST API
 * 
 * @param $media_id int
 * @return string
 */
function get_image_src_via_rest( $media_id = 0 ) {
    $media_id = (int) $media_id;
    if ( $media_id < 1 ) {
        return '';
    }

    $response = wp_remote_get( 'https://www.heretheweb.com/blog/wp-json/wp/v2/media/' . $media_id );

    // Exit if error.
    if ( is_wp_error( $response ) ) {
        return '';
    }

    // Get the body.
    $media = json_decode( wp_remote_retrieve_body( $response ) );

    return $media->source_url;
}

Now, inside your get_posts_via_rest function, you can call this new function to grab the featured image url.

$featured_image = get_image_src_via_rest( $post->featured_media );