Most implementations I have seen do much more than quaternions. How hard did you look?

Here’s an example you can play with in a browser, https://enkimute.github.io/ganja.js/

But what is implemented in computers is not 1:1 with the algebraic tools that can be profitably employed to solve geometry problems symbolically. GA is a rich language full of useful tools which can describe/model many kinds of problems.

Coming from a math background, let me recommend you start with https://arxiv.org/abs/1205.5935