How the Steering Wheel affects a Car ...

Ye gods. I'm not the best in this field by a long way and even I can see that is wrong in so many ways.

Alan

Clearly not. The history of 'sensitivity' in a photographic context is convoluted.
In a general context, 'sensitivity' refers to the size of stimulus necessary to cause a reaction, not the size of that reaction. The smaller a stimulus is necessary the higher the sensitivity. That applies both in general parlance and scientific/engineering usage. In that sense the ISO control does not usually change sensitivity of the sensor (if the sensor has dual conversion gain, it does, but not in proportion to the ISO). At some stage it crept into photographic usage to denote the size of reaction rather than the size of stimulus which went with the idea that 'gain' or 'amplification' changes 'sensitivity'. Generally it doesn't. Applying gain after a transducer does not change the sensitivity of the transducer. I suspect that the misunderstanding is due to radio hams, who are used to an RF gain control increasing the sensitivity of their receiver, but this is due to the specific behaviour of a diode detector - putting gain before the detector does change the minimum signal it can detect. In a sensor we are not putting the gain before the detector.
Anyhow, when digital cameras started to provide the ability to change the ISO, it was described (wrongly) as a 'sensitivity' control due mainly, I suspect, to this bogus RF receiver analogy. CIPA has been promoting this 'sensitivity' description for a long while, whilst ISO has been resistant, even though it adopted CIPA's two novel 'ISO' definitions in 2006. In the 2019 update of the standard it fudged the whole issue by adopting a term 'photographic sensitivity', which essentially says 'Photographic sensitivity is a term for ISO and for historical reasons sometimes it's just called sensitivity'.

That might be how it feels but it's very probably not true. Of course it depends on what you knew about ISO then.

Worse, it's actually the image plane. The focal plane is out there in front of the camera. I think it's a translation issue, where what was meant was 'plane of focus' and what came out was 'focal plane'. It's a consistent error in the ISO photography standards, so maybe it's not now an error.

It changes the input referred noise level, and thus the level of excitation which can be detected. Then, I suppose that any pre ADC gain does that. The key point with respect to ISO is that any actual sensitivity change is not proportional to ISO setting, nor is it mandated to be.