A 42” 900-1200 CFM insert, with a 10-12” duct, and a make up air system, are the mechanicals. Plus the services of a skilled cabinet maker to create the shroud around the insert, and finish it in something that will hold up to wear and tear. That’s after the electrician, HVAC person, and roofer have done their jobs, coordinated by the GC, to pass fire code restrictions about combustible surfaces. Which your inspiration pic would have issues with, and end up having that quartz backsplash all brown and scorched.

https://www.build.com/vent-a-hood-bh340pslb/s438831?uid=1038833

I just did a custom wood vent hood (different style, but same idea). You should look for a range hood insert-- they are designed to be covered in some way.

Just make sure the insert meets your range's requirements and your local building code requirements. The installation instructions and/or spec sheet for your range should tell you the size, CFM, and clearance requirements for the vent hood.