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.