@rhyolight Yes, there are both direct area connections and spreading /hierarchy connections.
The “Three visual streams” paper does outline the pulvinar/cortex connections but this is buried pretty deeply in the paper.
This paper does go more directly to these connections but it does start out with a dense presentation on the three-dimensional layout of the thalamus before getting to the connections:
If you go directly to figure 10 you get details of direct and indirect connections.