It's big but that's important for function. You have a beefy cooktop and I don't think you want to skimp.

What is the rim of the hood made of? I wonder if you could just paint the stainless part of it in the ceiling color to make it less imposing.

the kitchen will look nice painted. if doing a back splash, have them pull off that 4" piece up the back.

I like the copper strip. finding a better one to take it's place could be rather expensive. are you up for that? if not, I'd say just leave what you have. Or, see if you could veneer some tongue and groove wood strips around the stainless and paint it the same as cabs.

or, do some panels w/simple trim work and paint

you could also do a faux paint treatment to give it an aged copper look

if changing your hardware, make sure the holes are properly filled before painting. (just the drawers)

Leave it as is and for gods not clad in wood to make it even bigger . I too like the copper band so maybe pick that up with a nice copper bowl full of fruit on the counter

A more minimal hood would help

Would you change out this ceiling hood?

I would test it first for capture and containment using peanut or grape seed oil at the vapor point. The entry aperture looks a tad small for good overlap, but I don't have a good view from here. And I don't believe any information has been given about its air flow rate, or how make-up air is supplied. In other words, its performance could be as poor as one might expect from the design just above. In that case and if such performance is considered adequate, then going for visual minimalism at least addresses the aesthetics.