The house being cooled by aircon is within the same world as everything else is.

This doesn't mean that there's zero heat added locally (as many seem fond of suggesting): The compressors and circulation blowers and fans don't run for free, and every Joule of electricity they consume is ultimately converted to a Joule of heat in a process that wouldn't occur in the absence of aircon. That's not zero.

But in very broad strokes, it's not very significant. It's somewhat akin to running a refrigerator inside of a kitchen.

With aircon, the refrigerator is the size a whole house. That certainly sounds huge, and it is huge. But that refrigerated building is inside of a room that is the size of the Earth's atmosphere, which is very obviously vast in ways that kitchens simply are not.

It doesn't really matter. Millions of homes with aircon don't mean much when the atmosphere is millions of times bigger than they are.

Eventually radiates out into space ;-) It doesn’t disappear, but we don’t need to care much about infrared passing Alpha Centauri.