How should you place the Xbox Series X for maximum airflow? It doesn't actually matter which way you set it as long as you're not blocking the vents.
Despite being advertised as towering skyscrapers and monoliths, both the PlayStation 5 and Xbox Series X can lay on their sides to fit better in living room setups. The PS5 in particular is absolutely massive. The two consoles have different cooling solutions that dictate how you should place the systems.
Using Schlieren imaging, Gamers Nexus recently traced the airflow patterns for both the PlayStation 5 and Xbox Series X. The findings show negligible differences between the Series X's two orientations. It's all based around the Series X's negative pressure cooling system that pulls air from the bottom and exhausts it from the top.
Using a powerful 130mm fan, the Series X uses a kind of vortex to pull air upward and exhaust it in a pillar shape.
The video does an excellent job showing how the two consoles process airflow. The Series X in particular shouldn't be boxed in too much and that goes double for the back vents and the top exhaust. Gamers Nexus recommends you have the top facing the room and pushing air into the room itself if possible, but if its in a shelf, make sure to give the exhaust as much clearance as possible.