Getting a specific “title for a section” only on Startpage?

I think perhaps what you want is either

<?php if ( !is_front_page() ) : ?>
   <h2>
      <?php wp_reset_query(); ?>
      <?php echo $post->post_type; ?>
   </h2>
<?php endif; ?>

if you’ve done a custom front page that shows the blog posts, or

<?php if ( !is_home() ) : ?>
   <h2>
      <?php wp_reset_query();
      echo $post->post_type; ?>
   </h2>
<?php endif; ?>

if your front page is a static page and the post list is on a blog page or you have the vanilla setup.

This will output the post type heading on all pages that run the template except the home page or the front page.

or

<?php if ( is_page('my-page-slug') ) : ?>
   <h2>
      <?php wp_reset_query();
      echo $post->post_type; ?>
   </h2>
<?php endif; ?>

if you have this on some other specific page.