testing my camera which is about 7 years old ISO works pretty much like film. taking identical images, one with a longer shutter speed at ISO 100 and the other with a shorter shutter speed at ISO 1600 reveals zero difference in shadow details. diffing the images shows differences on the edges and in the midtones. likely due to increased noise in the ISO 1600 shot and some noise reduction code.
in other words my camera was engineered so that the ISO setting worked much like film ISO. the sensor is by modern standards pretty noisy, so the readout at ISO 100 leaves a lot low level signal behind (below the LSB) in favor of getting a clean signal. upping the ISO does indeed recover more shadow detail at the expense of reading out additional noise. then the software does god knows what, and in the end, it's a wash and ISO works a lot like film's ISO.
point is you can engineer these things to work any way you like. modern systems favor ISO invariance which, as a consequence, means that upping the ISO will treat shadow detail differently from opening the aperture or increasing the shutter speed. which, if you want, I suppose you can define "sensitivity" to mean "not the thing ISO does" and then you get to grump at videos.
if you care about shadow detail, or color fidelity, or highlight detail, or haptics, or how easy it is to clean the sensor, or any of those things it will behoove you to learn about your camera a bit. if you don't care about one thing or another, just let it slide.
ISO make pichers brighter.
if that's not enough detail for you do figure out what ISO does on your camera until you know enough to satisfy you. every camera is gonna be a lil differet.