Not all activities that earn Battle Pass points also earn Activity Points. However, you specifically mentioned Dungeons, which absolutely grant both. However, once you’ve reached the Battle Pass weekly cap, you cannot earn any more Activity Points either. But, you say you haven’t capped that? Can you show what you see in your Codex if you click the little treasure chest icon, like this…
And you say you have a red dot on the side. On the side of what?
Can you provide a link to some screenshots?