this implies that mathematics itself is not real, which has not been demonstrated at all.
Taboo the word “real”. What exactly do you mean here?
it is unconditionally true that, for example, the inscribed angle theorem follows from the axioms of Euclidean geometry
What is meant by “follows” is not unconditional. Implication is itself conditional on logical axioms.
However, empiricism doesn’t explain the relative simplicity of the mathematical axioms required to describe reality.
Our brains evolved in the reality and developped the kind of reasoning that is useful for it. No more explanation is required.
You are failing at the rationalist taboo game. Read this, please, and try again.
The word itself is just a label. The meaning is important. Try explaining the gears behind it, instead of comming up with a synonym.