Extractor hood: recirculation or exhaust air for KFW55?

We have a recirculation system in our current apartment.
Siemens extractor hood from 2015. Unfortunately, that thing is very loud, even on setting 1. I don't like it.

In the house, we have an exhaust hood from AEG from 2000. Very quiet on setting 1, on setting 2 still quieter than the recirculation hood on 1.
We are glad about that. For us, it's less about odors and more about moisture and possibly grease.

To our shame, I must admit that we often simply did not use the recirculation hood because of the noise.
The kitchen is open to the living room and interior without windows - a bad combination.

But nowadays there are surely better or quieter systems.

Due to the many supporters and further research on the internet, I have decided (if it is even possible) on exhaust air as it is actually the better option

Especially with an open kitchen with open living dining area and open staircase

Yes, noise level is also an important point with an open kitchen

The developer said I should just do it myself after acceptance. What is the worst that can happen?

Reclaiming of funding by KFW, provided you change your house by any measures so that your KfW level is broken. Applies for a period of 10 years. But I have never heard of an actual inspection...

In general, it should be noted that recirculated air is always louder than exhaust air. It also makes sense because the air has to be pushed through the activated carbon filters so that odor removal can take place. With exhaust air, the stuff just goes out.