What is technically happening when I increase the gain value? Are just the numbers coming from the sensor multiplied by a processor with a factor (e.g. x8 for +18dB) or is there something changing on an analog level (e.g. increasing the supply voltage of the CMOS-elements)?

It will be either amplification of the analogue signal level before the A to D converters on the sensor chip or a digital gain math added to the digital signal in the DSP. The supply voltages to the sensor etc remain constant. I suspect it is most likely to be added to the digital signals in the DSP.

I suspect it is most likely to be added to the digital signals in the DSP.
That would be great, because I realized that higher gain-values are revealing much more details in the shadows than lower ones (noise increases less with higher gain-values than useful picture-information). The gain-feature just being a computational multiplication would mean that the raw data from the sensor already contains all this shadow information independently from the gain-value. This would be one more hint that the 4k-raw-data from the FS700 will be awesome.