getCatsToTags.php

<?php #ВСТАВИТЬ В ФАЙЛ "archive.php" ?>

<?php if (is_tag()): ?>
  <?php foreach (getCatsToTags() as $category) : ?>
    <?php $anchor = get_the_category_by_ID($category) ?>
    <a href="<?php echo esc_url(get_category_link($category)) ?>" title="<?php echo esc_html($anchor) ?>"><?php echo esc_html($anchor) ?></a>
  <?php endforeach; ?>
<?php endif; ?>

<?php #ВСТАВИТЬ В ФАЙЛ "functions.php" ?>

<?php
/**
 * @param int $slice
 * @param bool|false $disableCache
 * @return array|mixed
 */
function getCatsToTags($slice = 10, $disableCache = false)
{
    $categories = [];
    if (!is_tag())
        return $categories;

    $getCatsToTagsCount = 'getCatsToTagsCount' . get_query_var('tag_id');
    $getCatsToTags = 'getCatsToTags' . get_query_var('tag_id');

    if ($disableCache) {
        delete_transient($getCatsToTags);
        delete_transient($getCatsToTagsCount);
    }

    $posts = get_posts(['tag' => get_query_var('tag'), 'post_type' => 'post']);
    $categoriesItems = [];
    $postsCount = sizeof($posts);

    if (get_transient($getCatsToTagsCount) <> $postsCount) {
        foreach ($posts as $post) {
            foreach (get_the_category($post->ID) as $category) {
                $categoriesItems[$category->term_id][] = $category->term_id;
            }
        }

        array_multisort($categoriesItems, SORT_DESC);
        array_map(function ($item) use (&$categories) {
            $categories[] = $item[0];
        }, array_slice($categoriesItems, 0, $slice));

        set_transient($getCatsToTags, $categories, DAY_IN_SECONDS);
        set_transient($getCatsToTagsCount, $postsCount, DAY_IN_SECONDS);
    } else {
        $categories = get_transient($getCatsToTags);
    }

    wp_reset_postdata();
    return $categories;
}