Both category and term are taxonomy. Taxonomy doesn’t have post type. Post type is related to posts/pages/attachments/etc.
When you assign a category to a post, you can’t say that that category has or related to specific post type.
If you want to receive post type of the first entity in the query, you will have to do something like this:
<?php
// fetch first post from the loop
the_post();
// get post type
$post_type = get_post_type();
// rewind the loop posts
rewind_posts();
?>