Air conditioning is amazing but uses a ton of energy, which is expensive and might eventually be unsustainable.
Evaporative cooling is the process of water separating into hot steam and colder water. Basically, evaporation is caused by a small fraction the water molecules moving at high speeds (which equals high temperature), which can be hot enough to effectively turn into a gas and leave the liquid body. When these molecules leave the liquid they take with it their above-average heat energy, leaving the liquid slightly cooler overall. This works well in arid climates because water in the air doesn't re-enter the liquid body, and especially well when it's windy out because the water molecules that evaporate are whisked away before they can condense.
A lot of people have evaporative coolers (swamp coolers) which cool you down by emulating sweat evaporating on your skin and use far less energy than AC. However, they actually slightly increase the temperature of the air and add humidity, which can be uncomfortable.
Enter: the two stage evaporative cooler. It harnesses the cooling effect of evaporation, but evaporates over a heat exchanger instead of your skin. The heat exchanger is used to actually cool the air in the building without adding any humidity and using very little energy.
The problem is that I can't find anywhere to buy one or any instructions on how to build one myself. I have some vague sketches on how I would build one, but I'm not sure how I would go about verifying the design and eventually building it. Does anyone know where I could find one? If they don't exist, is there any particular reason why? Am I missing a key complexity in the process?
Not a HVAC expert but I think larger commercial systems work that way you describe. Rather than describe it poorly, here's a link to manufacturers explainer for their evaporative cooling towers.
https://www.evapco.com/technologies/evaporative-cooling-101
I think these are often used to argument the condenser on commercial HVAC systems.