The gold and darker colors I'd prefer to be their own material, and the silver Kettle will show out at 50% Grey. Blender 2.92.0
You can use the image texture with different Color Ramps to drive all kinds of values. In my example, I've used Greater Than nodes to split the three grey values up to mix different colors created by Noise Textures. Of course you can use the mix factor to blend many more options or shaders.
I also used the image texture in combination with a Color Ramp for the Metallic input... I decided the gold and silver should be metallic = 1 and the etched part is dielectric = 0 (by the way, for realistic results never use values between 0 and 1, a surface is either dielectric or metallic, values inbetween should only be used for artistic / aesthetic reasons).
The Roughness is controlled by the image texture and a ramp, too. For the black/etched parts I made it absolutely rough by setting it to 1 in the ramp, the grey/silver part I made not too glossy with a value of 0.3 and the gold I made more shiny with 0.05 (of course you can also plug values into Specular etc.)
Last but not least I've used the texture for the displacement of course. I left it as it is, so the etched part is indented, the silver is the overall height and the gold is buckled up. Without a ramp or anything, the overall Scale in the Displacement also controls the range between the deep and the high parts. Put another ramp in there to change the relations to each other.
All in all you have to play around with those values, see what fits best and where to put the color stops on those ramps. A good way to start is take one ramp set to constant and use it to convert the greyscale image to three bright different colors like red, green, blue and see how you have to manipulate them so that they refer to the correct parts.
Then you can use this basic color ramp and give the stops the values you need or decide how you can address them for mixing factors etc. You dont need them to constant, but sometimes this helps to better outline the different areas (especially when you have antialiasing or artifacts).
EDIT: Here just two quick examples how an additional Color Ramp could be used to make extreme differences between the between highest and lowest displacement areas.
Or you could try to make the silver part look like it's brushed metal (just a quick setup, not meant to be perfect) by plugging some noise limited to the grey area in the Normal input of the Principled BSDF.