Wikipedia says “the property of "mass" is a manifestation of potential energy transferred to fundamental particles when they interact ("couple") with the Higgs field, which had contained that mass in the form of energy.”
A measure of a particle's energy as pertains to the spacetime curvature it induces
This is incorrect all the energy of a particle curves space.
Even velocity and potential energy.
Right, so those kinds of energy also induce spacetime curvature and are included in what I was saying
Energy, not mass. Photons also curve space in this way.