Even though it’s detached, I would definitely match the roof. The brick would probably be difficult to match, so I’d have it match the siding.

Yes, match the roof. Accessory buildings (garages, sheds, ADU...), always look nice when they match or compliment the main structure.

You have so much going on with your house's design that it would not bother me if the detached garage did not resemble it. Find a local architect that is willing to accept the challenge.

I would keep the garage simple, with a hipped roof to match the top part of your roof.

Does the brick wrap around the whole house or do you also have siding?

In my HOA we are required to match the existing homes roof line, materials and are limited by size. Are you under any restrictions?