That's not true. The quaternions are the even subalgebra of the 3D geometric algebra. They are not isomorphic. Quaternions are isomorphic to the set of scalars

That's not true. The quaternions are the even subalgebra of the 3D geometric algebra. They are not isomorphic. Quaternions are isomorphic to the set of scalars and bivectors in the 3D geometric algebra but the 3D GA also has vectors and a volume form. This is just like how the complex numbers are isomorphic to the even subalgebra of the 2D geometric algebra. The geometric algebra is richer, more powerful, more generalizable and more coherent than the quaternion algebra, all while being easier to understand because its so physical.