"Particles get their mass by interacting with the Higgs field; they do not have a mass of their own." Really?
In a Minkowski gravity field — otherwise known as an Inertial System — General Relativity predicts that gravity will exert a force on objects that force them to not "want" to accelerate. You can do the calculation yourself. The predicted geodesic motion of objects in inertial systems is that of a straight line with no change in speed.
Isn't that exactly what we call an object's "mass"? Yes. So it is gravity — that is, the graviton, that causes mass. It is an object's interaction with a gravity field that causes mass, not its interaction with a Higgs boson.
https://home.cern/science/physics/higgs-boson
Proving the Relativistic Energy-Momentum relation, the hard way and the easier way.
This adds the proof for the relativistic mass effects from motion, proving that gravity causes it.