To get the category of the current post you need to do this using wp_get_post_terms() inside of your post loop.
$terms = get_post_terms();
This returns an array that you loop over to get the images for each term, https://www.advancedcustomfields.com/resources/adding-fields-taxonomy-term/
foreach ($terms as $term) {
$image = get_field('logo_image', $term);
}