I did some work on a vending machine where we wanted to have something beside sharp square corners. We actually kept it mostly sheet metal, but they used custom dies (cost in the hundreds, not thousands) to create large radii (I think we did 3 inch). Depending on the shop you may luck out with them already having the radii you’re looking for. Still doesn’t allow super complex forms, but may allow you to create most of a form similar to what you showed.
To prototype before they committed to the die they approximated the bend with a series of slight bends close together. The term they used is “bumping” the bend. I think it some circumstances this may actually be a preferable way to create a bend if the radius or sheet thickness is too large.
A place I worked in college (https://www.kekdesign.com/shop) made large doors for some special low volume copiers using urethane casting. I think the run was around 100-200. They had a pretty slick setup with an injection machine and quick setting urethane, but I’m guessing it was still pretty expensive per part (though tooling was certainly way less than an injection tool). A recent client of ours was using urethane casting for their product with quantities in the dozens and I was surprised at how high the piece price was (different urethane vendor).