Search term is "digital linear scale". Even though they use the same hardware as the calipers, they are quite a bit more expensive. (Economics of supply & demand, I guess.)
Not sure how easy it would be to make your own. Ultimately you only need the long PCB the module slides on, but that might take a bit of trial and error to get right. Making the module as well sounds like a bit of a challenge.
When you factor in your time & effort making it work, it might not be worth it. For under $50 you can just buy-in a solution, or cut the end off a cheaper caliper.
Might be fun to strip one right down and see what makes it tick, though. Maybe there's a video out there already.