How to filter posts by post format “standard” from wp-json api?

This may not be the best answer but for the time being, I’ve been able to get what I want through querying again via a WP_REST_Request using the results I’ve got from the WP_Query mentioned earlier. So the full solution looks like this.

function get_blog_posts() {
    $posts = new WP_Query( array(
        'post_type' => 'post',
        'posts_per_page' => 4,
        'tax_query' => array(
            array(
                'taxonomy' => 'post_format',
                'operator' => 'NOT EXISTS',
            ),
        ),
    ));
    
    $ids = [];
    
    foreach($posts->posts as $post){
        $ids[] = $post->ID;
    }
    $include = implode(",", $ids);
    
    $request = new WP_REST_Request( 'GET', '/wp/v2/posts' );
    $request->set_query_params( [ 'include' => $include ] ); // because WP_REST_Request doesn't allow you to have query parameters inline.
    $response = rest_do_request( $request );
    
    $response = $response->get_data(); // You may handle errors too

    if (empty($response)) {
        return null;
    }

    return $response;
}

add_action( 'rest_api_init', function () {
    register_rest_route( 'unicorn/v1', '/blog_posts', array(
        'methods' => 'GET',
        'callback' => 'get_blog_posts',
    ));
});