What is the purpose of masking the LFSR value in STM32's noise generation?
According to section 14.5.1 of that same document the MAMPx[3:0] bits are used to control the amplitude of the generated noise (or triangle) waveform. For noise, they simply mask off (force to zero) the high-order bits of the LFSR output.

It seems pretty clear that the noise/triangle waveform can be used as a "dithering" signal for ADC operations, and that's what they have in mind with this feature.