I think running a data explorer query to identify exactly which topics fit the criteria and then getting the results sent in a recurring PM using Automation should do what you want.
Something like:
-- [params]
-- int_list :category_id = 4, 5, 6
WITH solved_topics AS (
SELECT p.topic_id
FROM posts p
INNER JOIN topic_custom_fields tcf ON tcf.value::int = p.id
WHERE tcf.name = 'accepted_answer_post_id'
AND p.deleted_at ISNULL
AND post_number = 1
)
SELECT t.id AS topic_id,
t.created_at::date "Created Date"
FROM topics t
WHERE t.id NOT IN (SELECT topic_id FROM solved_topics)
AND t.user_id > 0
AND t.deleted_at ISNULL
AND t.closed = false
AND t.category_id IN (:category_id)
AND t.created_at > CURRENT_DATE - INTERVAL '14 DAYS'
ORDER BY 2