Pretty much the same. Both Vulkan and WebGL can use GLSL directly (well, GLSL -> SPIR-V for Vulkan). WebGPU technically can't if you run it in a browser, but native WebGPU implementations can take GLSL, you can transpile, and finally you could just write WGSL as it's basically the same as GLSL, just with more Rust-inspired syntax rather than C-inspired.

Technically WebGPU and Metal support GLSL exactly as Vulkan supports it. You transpile. there is no difference except maybe you're used to that step with Vulkan and not with the others

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.