I have seen your Debian/Arch addendum, but since it’s meant to be easy and for simple media consumption only, how about Fedora Silverblue with a couple of Flatpak games for kids? You’ll barely have to look after it as it’s immutable, will update itself and the stock Fedora Gnome setup is pretty basic and simple enough for a smart kid. Plus he’s two- I doubt he will need anything outside of Flatpaks and a paint program.
Ooh ooh! I know this! Alpine! I run this together with MS-DOS on my Pentium 3, but FreeDOS should be no problem too.