Induction hob with extractor fan, unguided recirculation, experiences?

I see a planning error here. Cooktops with downdraft extraction are actually intended for installation in an island; not to be built under wall cabinets. The cabinets above the cooktop are likely to show swelling damage in a few years if pasta/potatoes/rice/soup is frequently cooked without a lid.

For understandable reasons (the customer wants it that way, and the kitchen fitter wants the sale), this planning error becomes reality as in your case. Uncontrolled recirculated air into base cabinets – preferably also on an exterior wall – in my opinion also leads to a horror show of an unpleasant kind.

I see a planning error there. The cooktops with integrated downdraft extraction are actually designed for installation in an island; not to be installed under wall cabinets. The cabinets above the cooktop are likely to show swelling damage in a few years if pasta/potatoes/rice/soup are frequently cooked without lids. For understandable reasons (the customer wants it that way, and the kitchen fitter wants the sale) this planning error becomes reality, as in your case. Uncontrolled circulating air in base cabinets – preferably also on an exterior wall – in my opinion leads to a horror scenario of the unpleasant kind.

Thank you for your opinion and also thanks to xmister The induction hobs can be installed under wall cabinets, according to the manufacturers Bora and co., this is no problem with a minimum distance of 50cm. Let’s say the kitchen was planned "privately," not by professionals, then the planner passed away, etc. a bit unfortunate circumstances but basically the kitchen stands as we wanted it. Meanwhile, I have seen that there is a continuous 1 to 2 cm high gap at the toe kicks anyway, since they are only clipped on. Is that sufficient for air circulation?

1 to 2 cm high slit is continuously present, since these are only clipped on. Is that sufficient for air circulation?

Yes, that is enough cross-section for the fan, no one sees the haunted house anyway ;)

Yes, that is enough clearance for the fan,
no one will see the haunted house anyway ;)

I can see now, absolute opponent of covering in the oven, right?
But that doesn't help me either. I try to get the best possible result and look forward to further answers/experiences.

In the left picture is the exhaust duct. It must be routed from the underside of the hob down to the plinth. So, it also has to go through the cabinet bottom. Normally, there would have been a cutout in the bottom at the back. If not from the factory, you now have to take matters into your own hands. The exhaust pipe can then either simply end in the plinth or be routed forward to an exhaust grille in the plinth. Without an exhaust grille, the exhaust will then spread inside the plinth of all cabinets and slowly escape through the slots (do not silicone). Personally, I have not yet found a sufficiently high plinth molding, so I don't have one yet, but when I do, I'll try it with the grille. It just feels safer to me.

We had it like that in the old house and had it installed the same way in the new one. With the only difference being that it is located in an island in our case. But also uncontrolled recirculated air. Most of it comes out at the bottom of the island despite the lack of a slot. You can feel it on your feet when the extractor is on a high setting. We never had moisture problems or "moldy cabinets." However, our experience only spans 2 years. We have drawers under the cooktop, which you would notice if water were condensing anywhere. So far, we have had zero problems in practice and cook almost every day, sometimes twice.
However, we have a controlled residential ventilation system in the house and an exhaust directly in the kitchen corner. I would highly recommend that combination. It distributes moisture in the house very effectively, which you can also tell by how quickly laundry dries in the utility room. And we have the cooktop from Bora; you can simply put the filter in the dishwasher without much effort. We do this regularly so that nothing gets greasy in the kitchen.