Neither Chrome nor the stable version of Safari (that ships to users), nor Edge, nor Firefox, will support WebGPU in its current form.
However, all browsers are actively working on a next generation API for high-performance, cross-platform GPU compute and graphics on the web (similar to Vulkan, Metal, and D3D12). If you're interested, please follow updates at the W3C GPU community group:
https://www.w3.org/community/gpu/