If you have access to user IDs, you can use the [count_user_posts()][1] function.

You would get the number of posts by a user like this:

    //Assume the variable $thisUser is equal to a valid user ID
    $ThisUserCount = count_user_posts($thisUser, 'recipe');

EDIT:
Where you're calling the count_user_posts() function, you're passing it the array $args instead of the post type, 'recipe'.

    <?php
    // 1. We define the arguments to define what we want to recover
    $args = array (
        'post_type' => 'recipe',
        'posts_per_page' => '16',
    );
    
    // 2. We run the WP Query
    // The Query
    $the_query = new WP_Query ($args);
    
    // 3. we display the number of messages and the authors!
    // The Loop
    if ($the_query-> have_posts()) {
        // THIS LINE WILL ECHO HOW MANY 'recipe' POSTS USER ID #2 HAS
        echo count_user_posts(2, 'recipe');
        echo 'recipes for';
        echo get_the_author(2, $args);
        echo '<br>';
        // THIS LINE WILL ECHO HOW MANY 'recipe' POSTS USER ID #1 HAS
        echo count_user_posts(1, 'recipe');
        echo 'recipes for';
        echo get_the_author(1, $args);
    
        // 3. We launch the loop to display the articles and the authors!
        // The Loop
        echo '<ul>';
        while ($the_query-> have_posts()) {
            $the_query-> the_post();
            echo '<li>'. get_the_title(). '</li>';
            echo '<li>'. get_the_author(). '</li>';
        }
        echo '</ul>';
    } else {
        // no posts found
    }
    wp_reset_postdata ();​?>

Also, your get_the_author(2,$args) function calls are not correct. get_the_author() does not accept any parameters anymore, and it only returns the Display Name of the author of the current post in the Loop.

  [1]: https://developer.wordpress.org/reference/functions/count_user_posts/