Query field Kunena new messages

Please see attachments. Debug does not reveal errors.

Is CB Code Field enabled within CB > Plugin Management? No idea what more to suggest as is working perfectly fine in all my tests across 3 sites.

That was the problem. The CB Code Field was not enabled.

I believe the code that gives you the number of NEW messages in Kunena might be this in:
libraries/kunena/forum/category/helper.php

"SELECT t.category_id, COUNT(*) AS new
FROM #__kunena_topics AS t
LEFT JOIN #__kunena_user_categories AS uc ON uc.category_id=t.category_id AND uc.user_id={$db->Quote($user->userid)}
LEFT JOIN #__kunena_user_read AS ur ON ur.topic_id=t.id AND ur.user_id={$db->Quote($user->userid)}
WHERE t.category_id IN ($catlist) AND t.hold='0' AND t.last_post_time>{$db->Quote($session->getAllReadTime())}
AND (uc.allreadtime IS NULL OR t.last_post_time>uc.allreadtime)
AND (ur.topic_id IS NULL OR t.last_post_id != ur.message_id)

Can you tell me how to put this in the code field.

You'll need to post on the Kunena forums regarding their API usage or review their documentation carefully. We can not help you with custom coding. CB Code Field is simply a tool to execute your code. What code you supply it is entirely up to you.