If your countertop is 3cm engineered stone, no brackets or additional support is required. If you're using 3cm natural stone and shorten your cantilever to 10" no brackets are required.

it would be 3cm Quartz, I was told at home depot that they wouldn’t install without support at 12 inches, same with another local seller

We used brackets from original granite bracket company. They have a lot of different options if you need l-shaped or straight from the front of the cabinets. The tricky part will be putting a bracket behind the sink. We have a range in our island and had to install a wall type of support behind the range so that the brackets would have something to grip onto, but our overhang was bigger than yours.

I recently put in a counter top that need support. www.countertopbracket.com, my contractor called them, great customer service they knew exactly what bracket would best suit our needs.

do you need the cabinet above the exhaust fan? imo you should pick a nicer exhaust fan that fits to the ceiling and lose the cabinet. the current fan in picture creates a weird overall shape under the cabinet.

ah, no the software program didn’t have the actual appliances, but it will be a Thermador Pro Cabinet mount vent hood. Sure I could have gone with a wall mounted chimney version but I prefer this one

"The tricky part will be putting a bracket behind the sink."

The best "brackets" on a job with cabinets like this aren't brackets at all. Square tube steel or aluminum run from the back of the cabinet fronts, let into the rear of the cabinets and flush with the cabinet tops on each side of the sink are best. Paint the exposed cantilevered ends; no knee-knockers.

There are steel suppotrs that can be used thea are invisble and that is what you need just as described above.

Steel angle supports can be installed on the underside of your island countertop. They should be invisible unless someone stoops down to look underneath. If you really want to be sure that the overhang is supported install fairly narrow legs on each end and connect them to an steel angle that spans from leg to leg. Good luck!