“Why do we call quantum physics an ab initio model? Why do we call classical mechanics an ab initio model? Is classical electromagnetism an an ab initio model (and if it is one, what are its first principles)?”
Quantum Physics is called an ab initio model because it follows Schrodinger Equation only. Similarly as classical mechanics follows Newtons Equations, we call it an ab initio model. Classical electromagnetism follows Maxwell’s Equations, so yes it is an ab initio model as well.