You have an exact example of the design. Take measurements. Determine the dimensions of the beam for width and height. Figure out how it will be finished so you can specify the material and construction. . .Then send the scale drawing and specifications to some more sources. Could be less money the more specific you end up.

Faux wood beams would be the easiest way to go.

https://www.homedepot.com/b/Building-Materials-Moulding-Millwork-Faux-Wood-Beams-Mouldings/N-5yc1vZc1mj

They come in a variety of dimensions and finishes. You'll still need a good carpenter to cut them and securely attach them to the ceiling but at least this can be done without the weight of real wood. From the floor you can't tell the difference.

Before you spend a lot of money to build a "simulated" heavy timber structure that could not exist in the real world, think about what you're simulating.

Real sloping timbers supporting a horizontal timber would not be stable so there would be a hidden part to the structure.

The simplest structure would be a traditional "Raised Tie" heavy timber truss (shown below) where horizntal and sloping ceilings have been installed at the tops of the timber members.

Of course the top of the truss doesn't need to be built but this approach allows you to detail the connections of the members in a more convincing manner: the horiontal tie would butt into the sloping member. You might even simulate a mortise & tenon joint.

Perhaps trim on the ceiling would satisfy a desire to add interest

without adding something that is obviously fake.