How to save a few hundred dollars, maybe
A friend commented that this had "made it abundantly clear I don’t have the foggiest idea how my air conditioner works". So here's an attempt at a quick primer.
The inside portion of an air conditioner is philosophically the same as the inside of a furnace - you're blowing air across a heat exchanger that either adds heat or takes it away from the air that passes across it. It's easy to heat things - but how to make them cold? You could use blocks of ice, or a Peltier thermoelectric cooler, but air conditioners take advantage of the fact that gasses become cooler when they're expanded. The secret to air conditioning is to use a special "refrigerant" that can, through expansion, become much cooler than the ambient air - and then, through compression, become much warmer than the ambient air. You can then blow a fan over the expanded gasses to pull heat out of the air in your home - and then blow a different fan outside your home over the compressed refrigerant to pull the heat back out.
Imagine that your air conditioner is the "sponge machine" I mentioned above, and that the sponges soak up heat instead of water. You bring a dry sponge into your house, you allow it to soak water from the air that passes over it, and then you take it outside. When you compress it, it can't hold as much water, so when you blow a fan over it it dries out quickly. You then allow it to expand again and return it to the inside of your house.
One more side-note: there's a pretty compelling theory that Air Conditioning was a key factor in the mid-20th century political shift within the US as more people left northern cities to live in southern states. See, for example, https://www.washingtonpost.com/made-by-history/2022/08/08/air-conditioning-remade-politics-now-its-key-navigating-climate-change/ and https://chicago.suntimes.com/politics/2014/8/20/18572909/how-air-conditioning-remade-america