Please, I need your help.

My goal is to create atmosphere in a scene: light is coming into a room and I want to see the atmosphere in this light: dust etc. And the air should be a bit "thick". I think you get the point.

How can I create that? I thought about using a light cone, but that looks artificial IMHO and destroys the whole scene.
My scene is lit by a HDRI map and a spot that I put far away from the scene's center, so that it shines through the window into the room.

Now all I need is the atmosphere.

Would someone help me, pretty please?

Thank you!