> I was consulting at a company that's developing a VR real estate app, and the first thing I did was check to see whether they were calculating their rotations with quaternions.

You had better checked whether representations are represented via spin groups (which can be represented via Clifford algebras). These work in every dimension in opposite to quaternions.

EDIT: And via pin groups (also representable via Clifford algebras), also reflections can be reprented (recall that the composition of two reflections is a rotation and any rotation can be represented this way).