The reading I was able to find explained that raising ISO will improve signal to noise ratio if the shutter and aperture remain constant, as you are increasing signal gain with the same amount of actual light.
Where as if you take an increase in ISO in order to drop exposure via either/both faster shutter speed or/and smaller aperture to maintain exposure, you are reducing the signal to noise ratio as while you have increased gain in the signal amplifier, you are reducing the actual light getting to the sensor - so relatively the signal’s noise gets more of a boost than the signal itself (incoming light).
I like to understand the science as best possible, but I did take up your recommendation to test as well.
The results corroborate the above statement very obviously, I went and set aperture and exposure first to avoid highlight clipping at ISO-12800 and took photos dropping 1 stop of ISO each time to ISO-800, with the shutter and aperture constant. Afterwards, I did another run set to avoid shadow clipping starting at ISO-800 up to ISO-12800. (RAW+JPEG)
I then brought the set in to Lightroom and did a quick slide on the exposure slider to brighten the darker images up and the darken the brighter ones to the other end’s level to see the results. What I got was overall the noise is fairly constant when pixel peeping, but what really stood out what that taking an image with ISO-800 that is very underexposed and having to brighten it, makes for a mess of grain/noise. Where as I can take an image from ISO-12800 that is overexposed considerably, and darkening it results in a much smoother image than the other way.
Going back to my prior mentioned images (the other set are of my buddy and his motorcycle, so I won’t post those) - my dog in our dimly lit hallway was also a lower overall contrast image, where as my buddy and his bike was shot on the side of a road, at night (10PM), with light bleeding over from the other side of the road’s parking lot. No tripod in either case.
Dog: EF70-200mm F/2.8 @ 125mm - 1/100s, f/2.8, ISO-6400
(perhaps ~1 stop underexposed result, histogram has room to either end.)
Bike: RF50mm F/1.8 (no IS on this lens) - 1/30s, f/1.8, ISO-6400
(perhaps ~1 stop overexposed result, histogram reaches both end of the scale with minimal clipping but heavy shadows - perhaps too much contrast here. His bike has a lot of chrome and I might have done well to try using a CPL.)
As well, I guess you are not going to notice color noise in the coat of a German Shepherd, but will in the solid colors of skin, clothes and a bike’s paint job.