Larger will be more functional. You also need lights. The recommended size for cxpture would be 36". Your cabinetmaker could outline the custom fabrication behind the doors.

The cooktop will be 30" wide... still need 36"? The appliance sales guy said 30" would be alright with induction.

I often use hoods the same size as ranges or cooktops I just up the CFM a bit but I do think the capture area needs to be as large as the cooking surface.

I would use the largest one that fits. There's no reason to use an insert meant for a 12" upper cabinet box when you have the depth for a deeper one. Width same, there is no reason to not go with the wider one if you are desinging from scratch.

Induction vs gas doesn't matter. It depends on what you are cooking and how often. Generally it s/b 6" wider than the cooktop. And ideally 6" deeper or as deep as you can get. CFM does not make up for capture area.

More: https://bamasotan.us/range-exhaust-hood-faq/