custom page for custom Taxonomy

The correct template to use in this case would be taxonomy-veranstaltungen-category.php, and that template needs to use the main loop.

So, at a bare minimum you should have taxonomy-veranstaltungen-category.php with the following code:

<?php get_header(); ?>


<?php while ( have_posts() ) : the_post(); ?>
    <?php the_title(); ?>
<?php endwhile; ?>

<?php get_footer(); ?>

That will show you the correct posts from the whichever category you select.