It's not quite there yet, but WebGPU will soon be a very good option for doing cross-platform 3D work. Using the native implementations you can run modern GPU code on Vulkan, Metal or D3D12.
Vulkan is already a very good solution for cross-platform graphics. It's possible to target Windows, Linux and Mac using Vulkan.
WebGPU is interesting, but I doubt that it will ever be able to compete with native graphics API's on pure performance because of the security considerations it has to take into account. I'm glad we will have a more capable alternative to WebGL, but it would be a shame if computer graphics were limited by the limitations of web.
The native implementation are generally planned to have options to turn off the more expensive security functionality.
WebGPU is also a much more ergonomic API than Vulkan. And as far as I know, there is no Vulkan-to-D3D layer, so you are relying on your graphics card manufacturer to supply a good enough implementation, which has not worked out great in the past.
> WebGPU is also a much more ergonomic API than Vulkan.
I really doubt that a JS/Typescript API is going to be better for graphics work than a C++ API. Game developers need every bit of performance available. They're not going to want to embed web technologies and the overhead which comes with them in their native apps.