Certainly. I heat a small flat (~35 m2) using just a AC unit and it works great: low costs, very comfortable. The only problem is increased dryness of the air.

But for a bigger place the setup is costly: you either need a couple units or a proper design, otherwise you'll end up with a only a portion of your home warm. Plus, AC units are still significantly more expensive than just a "trash-burner" type of furnace that is the most popular.

Electric heat should be the cheapest form. That would end a lot of air pollution that is a very serious health risk in Poland.

Look for the most efficient heat pump. As I understand, the co-efficient of our heat pump is 2. (Geo-thermal is 4.) Electric heat is 100% efficient, wood up to 75%, gas heat up to 70%.

Modern gas furnaces can achieve over 90% fuel efficiency.

So for resistive heating (where electric tops out at 100%), it's likely that a home furnace is converting more of the fuel into heat in the home than the combination of the power plant and electric heater.

An easy gut check for this is how much cheaper natural gas is to heat with than resistive electric. As a sibling comment says, a heat pump really improves the numbers for electric.

Right, a coefficient of performance (COP) of 1 is equal to 100% efficiency. A heat pump typically exceeds that, so your COP 2 heat pump is 200% efficient (useful heat divided by work required). If an electrical joule cost the same as a natural gas joule, the heat pump would definitely be more economical; but in real life it's not so straightforward.

If you're running your electric heating from a natural gas-fuelled power station, which has an efficiency somewhere along the lines of 40% (if you're lucky), then using a heat pump with a COP of 2 means you are heating your home with 80% efficiency. Modern gas central heating systems can be >90% efficient.

Alternatively, if you go by the relative price of electricity compared to natural gas, typically electricity has three times the price for the same amount of energy. In that case, you would need a heat pump with a COP of >2.7 to make heating cheaper than using a gas burner.

Such heat pumps do exist now. The benefit is that if/when the electricity grid transitions to renewables, you are sorted.

you can go as high as 4 in most heat pumps. Obviously, it strongly depends on the outside temperature. But if it's above 4 degrees C, you should be fine.