AIの助けを借りて、自分のコンテキストに合ったものが機能するようになりました（solved 参照を調整する必要があるかもしれません）。
他の人もこのソリューションを利用できるかもしれないので、最終的なソリューションを共有します。
最初のイテレーション:
-- [params]
-- date :start_date = 2024-01-01
-- date :end_date = 2024-01-19
SELECT
c.id AS category_id,
COUNT(DISTINCT t.id) AS topics,
COUNT(p.id) AS posts,
SUM(p.like_count) AS likes,
SUM(p.reads) AS reads,
COUNT(DISTINCT CASE WHEN tf.name = 'accepted_solution_id' THEN t.id END) AS solutions,
COUNT(CASE WHEN p.reply_to_post_number IS NOT NULL THEN p.id END) AS replies
FROM categories c
INNER JOIN topics t ON t.category_id = c.id
INNER JOIN posts p ON p.topic_id = t.id AND p.post_type = 1
LEFT JOIN topic_custom_fields tf ON t.id = tf.topic_id AND tf.name = 'accepted_solution_id'
WHERE p.created_at BETWEEN :start_date AND :end_date
GROUP BY c.id
ORDER BY COUNT(p.id) DESC
私の特定のユースケースの最終ソリューション:
-- [params]
-- date :start_date = 2024-01-01
-- date :end_date = 2024-01-19
SELECT
c.id AS category_id,
COUNT(DISTINCT t.id) AS topics,
COUNT(p.id) AS posts,
SUM(p.like_count) AS likes,
SUM(p.reads) AS reads,
COUNT(DISTINCT CASE WHEN ua.action_type = 15 THEN t.id END) AS solutions,
COUNT(CASE WHEN p.reply_to_post_number IS NOT NULL THEN p.id END) AS replies
FROM categories c
INNER JOIN topics t ON t.category_id = c.id
INNER JOIN posts p ON p.topic_id = t.id AND p.post_type = 1
LEFT JOIN user_actions ua ON ua.target_topic_id = t.id AND ua.action_type = 15
WHERE p.created_at BETWEEN :start_date AND :end_date
GROUP BY c.id
ORDER BY COUNT(p.id) DESC
