I repeated the same measurements with another spectrum analyzer, the Agilent35670a
This instrument spectra are much cleaner, I did only 32 averages instead of 256 with the Yokogawa sa2400
First plot: gain 1000 in-loop pd: PM100D
Second plot: gain 1000 in-loop pd: DET10N
Third plot: gain 5000 in-loop pd: DET10N