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The ingredients for fusion reactors (deuterium, tritium and helium-3) are rare, not fully reacted intermediate byproducts of the proton-proton cycle that powers the sun.

The likeliest case for a Dyson Sphere civilization would be some sort of solar powered Gray Goo von Neumann replicator.

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The ingredients for the most primitive, low-tech, hayseed fusion reactors are sort of rare. But anybody with any sophistication at all has no need for such primitive processes. They fuse plentiful regular hydrogen, helium, and, not to be wasteful, whatever they get from fusing those, too.

In theory you can fuse up to Iron.... the last stage of stars. You are not limited to just Hydrogen.

I assume that some of fusions done by the star are net energy consumption (i.e. not usable for energy production)

You assume wrong. Anything beyond iron is made in a supernova, i.e. in the last moments before it is not really a star at all, anymore.

takes a star's worth of gravitational force to push atoms like those together in the core to produce fusion.

To reproduce such heavier elements in fusion reactors on earth would require, likely, a much higher energy than the output.

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