WordPress the_category(); only works with message-posts not with project posts, how do I specify project categories?

the_category and wp_list_categories are for the category taxonomy term. What most people call a category is most likely a taxonomy. Category is just a default taxonomy for the post post type.

You need to use the general taxonomy functions such as the_terms and get_the_term_list.

echo '<li>'; echo get_the_term_list($post->ID, 'project_category'); echo '</li>';

You will need to change project_category to whatever custom taxonomy name you have used.