Ehh from the user's perspective sure, but under the hood it's different.

Vulkan you're doing GLSL -> SPIR-V

WebGPU you're doing GLSL -> WGSL -> (HLSL->DXIL) / (MSL->IR) / SPIR-V / GLSL (for the compact backend)

Then the driver takes GLSL/DXIL/Metal IR/SPIR-V/etc and produces it's own bytecode. Different copies of LLVM are involved a few different times in different places. It's a complex and frankly fairly crappy pipeline.