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.
i installed mine myself and probably illegaly. But its super easy and those people who install it do a shit job sometimes. I watched professionell people flushing those pipes with compressed air....
And the fine is nonexistent so everyone should do it themself.