Regarding how to derive Maxwell’s equations from QED, I’d recommend this lecture: https://theoreticalminimum.com/courses/special-relativity-an...

This derivation is in the context of classical field theory, but QED is only a short hop away through path integrals.

It’s quite remarkable how the complexity of Maxwell’s equations can be reduced to a single term in the Lagrangian - (F_uv)(F^uv), assuming no charges. That’s really it!