SolveSpace is available in library form. It uses NURBS to represent surfaces, with triangles as a fallback.

https://solvespace.com/library.pl

Notably the library was used (at least for a while) in the development of Dune 3D:

https://dune3d.org/

but then the author used the source directly as noted in the Github footnote:

>I ended up directly using solvespace's solver instead of the suggested wrapper code since it didn't expose all of the features I needed. I also had to patch the solver to make it sufficiently fast for the kinds of equations I was generating by symbolically solving equations where applicable.