Why do we call quantum physics an ab initio model?

because:

It starts from fundamental postulates (e.g., the Schrödinger equation, the superposition principle, the probabilistic interpretation of the wavefunction).
These postulates are not derived from experiment, but rather are consider to be true.
Once the postulates are accepted, everything else (atomic structure, chemical bonding, etc.) can be derived mathematically.

Why do we call classical mechanics an ab initio model?

It is based on Newton’s laws of motion, which are taken as first principles.
From these laws, one can derive the motion of objects, conservation laws, and even celestial mechanics.

Is classical electromagnetism an an ab initio model (and if it is one, what are its first principles)

Maxwell’s equations, which describe how electric and magnetic fields behave and interact.
Lorentz force law, which describes how fields act on charges