Yes, especially Highs is completely unrelated because it's for (mixed integer) linear programming problems and quadratic programming problems, so it's not able to solve the types of problems described in this manuscript.

IPOPT is a bit of a stretch but I do know that there are some people in the mathematical programming space that use IPOPT's constraint satisfaction piece for solving a nonlinear system in a pinch, but it's not the main use case of IPOPT which is nonlinear optimization with nonlinear (in)equality constraints. This case has no optimization and is just nonlinear equality constraints, which you can then specialize quite a bit on. But while it is considered common knowledge in numerical circles to not use a nonlinear optimizer to solve nonlinear systems, I don't have a good canonical benchmark to point to on that, so we might as well make this it.