I do have a WebGL-based implementation of FFT, but here I used good old JS. When properly written, it gets translated into really fast machine code, which is even faster than WebAssembly (I tried!). WebGL's problem is the high toll on the CPU--GPU bridge. When you need to transfer a block of audio data from CPU to GPU to perform calculations, you wait. When you need to transfer the FFT data back, you wait. These waits quickly outweight everything else. However on wavelet transforms GPU comes first because you can store some pre-computed FFTs on GPU and reuse them in multiple runs.