> Given that the plasma is several million degrees, it will radiate a lot of energy

That doesn't entirely follow. 2 particles whizzing past each other at relativistic speeds have extreme temperatures but don't offer much energy. Mass is in this equation.

What if you have 10^20 particles? Each charged particle emits photons with energy/frequency proportional to their speed (Bremsstrahlung). This is mostly from electrons because they are much lighter and so are much hotter/faster. Plasmas are quasineutral though so you'll have those electrons present. There is a long line of research trying to get away from that constraint with little luck so far (but it should continue to be worked on!).

Jumpjng back up the stack: photon radiation is mostly considered a loss since it transfers energy out of confinement and does not impart it on other fuel. You nominally extract your heat via neutrons: same as fission reactors. Some designs (Helion) aim for reactions with charged byproducts. The reaction produces a current that can be coupled by a surrounding coil, much like a transformer but powered by current induced by plasma rather than another copper wire.