If you make a screenshot of a YT video there are two problematic points connected with colour management: 1) even if you view YT in a colour-managed browser like properly set-up Firefox, video is not colour-managed – you’d have to download the video and watch it on a colour-managed video player (on Windows there’s MPC-HC, on Linux I know that the default Linux Mint video player respects the monitor profile); 2) the screenshot app might not be colour-managed, so you need to assign your monitor profile to the screenshot file.
OP could look at how Harry Durgin (referenced above) tackles skin tones in dt.