a lot of the ac units you see in Korea use water to heat and cool air (sometimes they have settings for dehumidifying or just fan), and I believe most of the ones you see in Korea are split units that need connection to an outdoor unit (some a/c do come together with the indoor unit and outdoor unit, or you can get just the indoor unit if you already have an outdoor unit too). the wall mounted ones are usually split units. If you can't install an outdoor unit, I would probably suggest a standalone portable ac. a downside to those units is that you have to drain the water often, but they're not as loud as you think.
thank you. :)