What does the Activity column exactly refer to?

The Activity column always refers to the activity on the latest post in the topic.

In “Web activity”, the first post is the last post, so when it’s edited the activity date is changed. In “Carry forward responses”, the last post is “listed”, so an update on the first post is not an update of the last post and because of that the activity date doesn’t change.

You could delete those small action posts.