Current kitchen planning - kitchen purchase

Can someone briefly explain to me again whether one should use exhaust air or recirculated air with the hood? I always assumed, hole in the wall and exhaust air outside. Other opinions now say that a lot of warm air goes outside with that. So what do people use nowadays in a new building?

Which heating? And controlled residential ventilation?

Have the same question.
With us, air-water heat pump (Stiebel Eltron LWZ 304 Trend) including controlled residential ventilation.
Tend to go for the recirculation hood

Which heating? And controlled residential ventilation?

Heat pump and controlled residential ventilation (energy-efficient house 55)

We decided on a recirculation hood, partly because of the otherwise necessary special wall breakthrough and the loss of energy due to venting outside. On the other hand, it would have looked awkward with our kitchen otherwise.

It has to be a good hood, with an activated carbon filter. We chose a Berbel; it made a very good impression, but I can say more in a few weeks.

We currently have the Miele DA 6096 W Black Wing in the planning. My wife liked that you don't need a chimney going up to the ceiling here. I just saw that it is available as [Ab- und Umluft].