Search for solution range hood

We have the cooktop on a peninsula and do not have a range hood (since cooktop including downdraft extractor is not available). So far, it works well by tilting the window 10 minutes before and leaving it tilted for 10 minutes after cooking. So we will continue without a range hood for now, as we believe that recirculation hardly does anything anyway (at least we never used it in our apartment, always just tilted the window). Exhaust air is of course a different matter...

Mmh... well, everyone can do as they please. I am also pro exhaust air. But one should note that the extractor hood/downdraft serves various functions. - Odors - Humidity - Fat particles (I think that's the term in technical jargon :D ) With two windows tilted, you might (!) have a chance to reduce humidity and minimize odors. But that primarily depends on cooking behavior. Someone who only cooks pasta will probably be fine with that. Someone who stews and especially sears at high heat rather less so. A controlled residential ventilation system might help. But a big problem is the fat particles. Especially when searing. These are the fine fat droplets that rise into the air. They carry bad odors and are also disgusting when they settle on surfaces. An extractor hood sucks them away. Some better, some worse, but they go away. With recirculation, they get caught in the carbon filter; with exhaust air, in the stainless steel filter or get blown outside. Therefore, if I intend to actually use the kitchen for cooking, I would definitely consider the type of extraction method.

So we will continue without a range hood for now, because we believe that recirculation hardly has any effect anyway (at least we have never used it in our apartment either, always just tilted the windows instead).

With a proper hood, recirculation makes a big difference. For example, it prevents grease from the stove spreading all over the place.
Put a deep fryer under a good Berbel (or similar) hood. Then you'll know what a proper extraction with a kilo of activated carbon really does. You won't need an open window anymore.

It's called grease fog. Otherwise, exactly what and wrote is correct. 1. Windows alone are not enough, unless you want to do a thorough cleaning after every single cooking session! 2. Recirculation hoods that are not from the very lowest price range can extract quite a lot.

There is also the table lift hood from Berbel. Nothing hanging around in the room, free choice of cooktop, and it disappears when not in use

They are not only available from Berbel. Siemens also offers stylish and functional ones... as well as other manufacturers in the price range from 300 EUR upwards.

So far it works well to tilt the window 10 minutes before and leave the window tilted for 10 minutes after cooking.

That's quite a statement when it comes to saving energy ;) Has the OP not answered the questions yet? Am I seeing that correctly, or where should one look?

Open kitchen or closed?
Wood stove yes or no?
Size of island?
Preferences?

Kitchen is open.
No wood stove.
Island is about 370x120cm in size.
I have no preferences.