The AlphaSmart 3000 has a backup battery, so that it doesn't lose your texts when you replace the regular batteries. You can actually see it through the translucent case – it's right above the “end” key. It's a regular CR2032 button cell, the type that's still widely used, e.g. in the Apple AirTags.
My two AlphaSmart devices came with working backup batteries. One of them even held on to texts that the previous owner had written on it. But since I didn't know how old they really were, I decided to replace them both. Which, fortunately, is a pretty straightforward process.
So it turns out I was making things much more complicated than they had to be – again.
After writing on the AlphaSmart some more and transferring the texts over to my MacBook Air, I found a few issues. Some keys couldn't be mapped correctly, eg. the +/= key. And sometimes, it appeared as if BetterTouchTool would stumble and fail to properly remap a key. So I decided to take a step back and look at things all over again.
tl;dr – you don't need BetterTouchTool or Karabiner or any other third party software. MacOS can do it all by itself.
I came across the AlphaSmart devices by accident, via a post on the Fediverse somewhere (sorry, can’t remember by whom or when exactly). I was immediately fascinated and, just hours later, was already bidding on two devices on eBay. Two, in case one wouldn’t work. Turns out they both do, but they are also slightly different. More on that below.