They're called retro handhelds and you can get them for ~$30-40 at the low end, which can apparently run up through Playstation 1.

In the $200-300 range (so still less than a Switch 2), you can apparently run up through Switch and maybe PS3.

I know about these but they require a lot more technical know-how to set up and getting ROMs is legally questionable. Your kid's friends are probably not playing those games either. They aren't a good option for most people.