I installed mini splits (small heat pumps) in each of our rooms. Everyone gets their own temperature and they were only 800$ a piece. Did installation myself and it was pretty easy. Hardest thing was pulling a vacuum in the lines before releasing the freon (or whatever it's called) but all I did was watch a youtube video. They've been going strong for several years. I looked at the prices and they are still the same.
BTW, in Germany you're not allowed to install it yourself. At least that's what I read some time ago. I guess nobody checks, of course, but in case things go bad and you need insurance, probably they can invalidate it due to the fact you did something illegal.
Not saying it makes sense, though.
Did the same. air air is cheap and works like a charm. this 40k for heatpump is for the most luxury version every salesmen trys to sell