I second this if he can find a 2013~2017 for free/cheaper, I use an old Macbook Air with EndeavourOS mostly for writing, but my use case is not that far from OP’s, it also runs some old games.
It is light and portable, and it is just as easy to find a refurbished option as the Thinkpad (at least in NA).
My only problems are with the drivers(the Wi-FI and the FacetimeHD camera) and the charging cable.
I tried a bunch of distros, but only with EndeavourOS I got them to work easily.
That said, if OP prefers better Linux support, and better cost x performance. He will be better suited with a Thinkpad T or X (T480/T490 or X280) refurbished will be in the price range.
X280 is barely above 1Kg, with a smaller screen.
T480 is chunkier, bigger screen and Ethernet port.
Start with building a very cheap computer with your kid.
You can buy parts for cheap or sometimes get them for free from e-waste processing places. You can do the screws to the case, but let the kid put the parts in place while you explain what they do.
Parts are easy to handle, just make sure to not damage the components as they look cute and are a bit malleable, but put too much pressure you can destroy it (not sure a kid will be strong enough for that).
It is as easy as building Lego, or putting a cartridge on an old console. This will help to make the computer less scary.
Make sure that you can do it yourself and test the parts first before involving your kid, so they do not get too frustrated if it fails.
This will cover hardware.
You can also help them to install the OS.
After, make a list of the programs you want your kid to be aware of: calculator, place to write text, anything you think it will be useful. Take some time to explain them, and do some exercises with each - let’s write a letter to a friend, etc… Let them play around with it without judgment. (remove things you don’t want them to use).
If you want to give the child some background in how software works, Logo was very popular with kids at the school.
Logo is this little turtle that you give orders, similar to imperative programming language used in most softwares.
And the turtle would draw a green line on the screen.
There are plenty of options for software that provides that, here is an option https://apps.kde.org/kturtle/
And, of course, try to break these in multiple days, building a PC, installing OS and playing with programs can be overwhelming for some kids.