How can I generate a list of post-type specific categories?

You can create a template page and use the WP loop: taxonomy-{taxonomy}-{term}.php
https://developer.wordpress.org/themes/template-files-section/taxonomy-templates/

Or you can use the get_posts functionality: https://codex.wordpress.org/Template_Tags/get_posts#Taxonomy_Parameters

Something like this maybe:

    <?php
      $args = array(
         'posts_per_page' => -1,
         'post_type' => 'reports',
         'my_custom_taxonomy_name' => 'education',
         'post_status' => 'publish'
     );

    $show_albums = get_posts( $args );
    ?>

This will return a list of posts in that category, you can then display them on the page.