Scientific discovery is learning new facts about the world. Inventing new contraptions to help us in our goals is technology. I.e. I don't think anyone would call Henry Ford a scientist or Albert Einstein an inventor. I thought it's basic and well-understood distinction.

If you follow the constructivist philosophy of science (spoiler alert: I do) then absolutely Albert Einstein is an inventor. He invented a mental model (essentially a lossy compression) of some parts of reality that better fit observed phenomena than its predecessor. Our mental/scientific models are not descriptions of reality; objective reality is unknowable. What they are, are tools (technologies!) that we can use to predict effect, given a cause and a state.

Is constructivist philosophy of science an independent axiom or does it have testable predictions? E.g. is there a function from theorems of ZFC to {invented, not invented}?

it's a philosophy, so no it doesn't have testable predictions - but neither does objectivism, its counterpart. But then, testable predictions don't tell you about the nature of reality so c'est la vie.

> is there a function from theorems of ZFC to {invented, not invented}?

Can you derive definitions of inventions versus discoveries from set theory? No, probably not. You can't derive the smell of a rose from set theory either though so it's probably not a very good theory of everything.