As I mentioned, unnormalized quaternions just adds an extra uniform scaling, so it’s just a matter of dividing the final vertex by qq* to remove the scaling.
EDIT: I guess if you use a shitty overzealously reduced version of the quaternion formula then you absolutely need to normalize it constantly, because the reduced formula assumed three degrees of freedom (completely defeating the purpose of using quats in the first place), normalization is then to solve a problem that you caused. But if you use a proper formula then my recommendation is actually that you never normalize your quats, instead only un-scale your vertex at the end.
EDIT: I guess if you use a shitty overzealously reduced version of the quaternion formula then you absolutely need to normalize it constantly, because the reduced formula assumed three degrees of freedom (completely defeating the purpose of using quats in the first place), normalization is then to solve a problem that you caused. But if you use a proper formula then my recommendation is actually that you never normalize your quats, instead only un-scale your vertex at the end.