For me ab initio means we are calculating the behavior of a system from a set of assumed fundamental laws.
Therefore, quantum mechanics is considered an ab initio model as the calculations start from its fundamental principles. (for example one can start from the Schrodinger equation or path integrals)
Classical mechanics is, in my opinion, more of a theoretical framework rather than a real ab initio model. It provides an ab-initio framework when the forces/potential are themselves specified from fundamental laws. The necessary forces could be obtained from an empirical/interatomic potential (possibly also through quantum mechanics).
Classical electromagnetism is in a similar boat as classical mechanics. Maxwell’s equations aren’t “fundamental” in the same sense as quantum electrodynamics.
In the end what you call ab initio always feels a bit relative to what you are doing.