How do I get a list of all categories that a given user has written blog posts for?

Question

As, much as I know about WordPress we have to ways to achieve this.

First: You have to retrieve all posts written by an author an then you can fetch categories assigned to those posts. Store them in an array uniquely.

$args = array('author' => $author->ID, 'posts_per_page' => -1, 'fields' => 'ids');
$authorArticles = get_posts($args);
$postList = array();
foreach($authorArticles as $key => $article){
    if(!in_array($article, $postList)){
        $postList[$key] = $article;
    }
}
$termsList = array();
$siteURL = site_url('/category/');
foreach($postList as $article){
    $terms = get_the_terms($article, 'category');
    foreach($terms as $term){
        if(!isset($termsList[$term->term_id])){
            $termsList[$term->term_id] = ['term_id' => $term->term_id, 'term_url' => $siteURL.$term->slug];
        }           
    }
}
echo '<pre>', print_r($termsList), '</pre>';

Second: As, suggested by @Jacob you have to use SQL for retrieving list of categories.

Best Regards,