Is an air conditioner with a heat pump function worth it?

To my shame, I have to say that until now I had only looked for inverters and the shops only offered those as well.

I could be wrong, but I believe that nowadays - at least in the private sector - there is only inverter technology.

The inverter is a simple frequency converter that can control the power of the compressor in the air conditioning system as needed.

No more and no less.

The rest of the system is absolutely identical to a "simple air conditioner."

Inverter systems can be controlled much better, the regular ones can only be on or off. I would recommend this for high air conditioning usage, but it is more expensive. Except for the cheapest ones, all should be able to heat. The compressor then just runs in reverse.