When I was the hiring manager, I’d hire engineering degreed people and round file any dual majors that included business. A course or two was OK but I wanted engineers.
An engineering manager has to be well schooled in engineering before becoming a manager. Besides, engineering management isn’t really business its people management, a totally different skill.
My company would hire business people to handle the business side of things. If you want to go into the business side, then do so.