Dadas dos tablas, seleccione todos los datos de una tabla y solo los más recientes de la otra

Primero busque la última publicación en cada categoría:

select topic_cat, max(topic_id) as latest_topic
from topics group by topic_cat

Luego añádelo a tus condiciones de unión:

SELECT  c.cat_name AS Category, t.topic_name AS Recent_Topic 
FROM categories c
left JOIN topics t on c.cat_id = t.topic_cat 
left join (select topic_cat, max(topic_id) as latest_topic
        from topics group by topic_cat) as latest_topics 
        on latest_topics.topic_cat = c.cat_id
        and latest_topics.latest_topic = t.topic_id 
where latest_topics.topic_cat is not null or t.topic_cat is null;