It is to be considered independently. Gas usually has a low initial investment. Heat pumps are mostly more expensive because everyone involved profits. I personally cannot say anything about controlled residential ventilation. Researching online, those against it are often the ones who don't have it, and those who have it hold the opinion that it is absolutely necessary. It is energy-saving, but it often pays off late. However, there is always fresh air and no more ventilation obligation. You should plan for about €10,000 for it. If I were to build anew and had the money for it, I would install one.