They feel pretty close to shipping this to me:
https://webkit.org/blog/14879/webgpu-now-available-for-testi...
They recently shipped an update that resolves all issues running PlayCanvas' WebGPU backend. My guess is that we're looking at 6-12 months to reach production.
To track WebGPU support, I recommend this awesome site:
https://web3dsurvey.com/webgpu