I needed headless Chrome running website with WebGPU enabled and meet same problem as you and seems solved it.

Tested on openSUSE Tumbleweed

google-chrome-stable http://localhost:3000  --enable-unsafe-webgpu --enable-features=Vulkan,VulkanFromANGLE --headless --remote-debugging-port=2500 --use-angle=enable

Beta, Unstable and Canary channels doesn't need --enable-features=Vulkan,VulkanFromANGLE.