white-noise | A simple white noise generator web audio component | Speech library

the Fourier transform of white noise is white noise

This is true, but it does not mean that they are axactly the same - otherwise there would not be much point in doing the FFT.

If you plot s and the real part of fft(s) you will see that the transformed noise has much higher values.

Conversely, if you fill gaussComplex with random values of standard deviation 1, the inversely transformed noise will have a much lower standard deviation. This is what you observe.

To generate the FFT of Gaussian white noise in the frequency domain you need to scale it correctly. In your case, this should do the trick: