How can I show the author’s latest post with title?

As you already have the author’s ID, you can create a new WP_Query and get the 3 latest posts of the Author.

The following code will do the job for you,

$getPosts = new WP_Query(
    array(
        "author"         => $user->ID, // This tells the query which author's post you want to get.
        "posts_per_page" => 3,         // This tells the query how many posts you want. In your case, 3.
        "orderby"        => date,      // This tells the query that you want the posts according to their publish date.
        "order"          => "DESC",    // This tells the query that you want to get the latest posts. If you change it to "ASC", then the query will get the oldest posts.
    )
);
if($getPosts->have_posts()) {
    while($getPosts->have_posts()) {
        $getPosts->the_post();
        echo "<h2 class=\"post-title\"><a href=\"" . get_the_permalink() . "\">" . get_the_title() . "</a></h2>"; // Echo the post title as a link to the post on the page.
    }
}