ᐅ Looking for a solution for a range hood ventilation system

There are also downdraft extractor fans available for less than 3000€ for Bora, as already mentioned.
It’s important to remember that downdraft extractors usually come with the induction cooktop included.
What is the budget for the cooktop plus the hood?
Depending on that, the question might become irrelevant…

I can recommend the Elica Switch.
In use since 2019, with me!

A well-known Swedish furniture store offers a recessed cooktop for 1600 €.

Take a look at Falmec Mare, available in black and white, and you can choose the hanging height freely. In my opinion, it is stylish, functional, and should fit reasonably within your budget.

We also have an island and chose a Miele induction cooktop with an integrated downdraft extractor.
We had the builder install a large exhaust duct directly into the floor slab and routed it out on the north side.
It works perfectly. Almost "all" odors are captured and vented outside.
I would definitely do it again. We initially considered a ceiling-mounted range hood and even had a ceiling reinforcement planned, but for aesthetic reasons, we ultimately decided on the downdraft extractor.