I got an air to air heat pump that heats and cools my living room. Heat spreads up in the winter so the top floor is also covered, the cold going down in the summer is fairly useless to me since I don't use that part of the house much, but it's still a thing.
Just have this thing on my wall:

And the outdoor unit too of course.
For actual heating of the whole house I'd need ground to water which isn't as good for cooling, but that would be like 30k euros installed, this one was a bit over 2k and still helps me burn less wood in the winter too.