I presume that the fungi grow toward the source of radioactivity until they engulf it, and it is not destroyed, but instead segregated and more easily separable from the environment by bio-accumulation.
I.e. if you seed radioactive soil with radiotrophic fungi, wait a few years, and then mechanically separate fungus from soil particles, the separated soil would be less radioactive than it had been previously.
The fungus itself will be more radioactive than background.
I don't believe neutron activation is significant anywhere on Earth outside the containment of a fission reactor, power research facilities, or nuclear bomb tests. So mostly, places slowly become less radioactive over time unless you get radioactive particulates from one of the aforementioned sources, or from a natural concentration, and release them into the environment somewhere.
Bio-accumulation can occur, such as the naturally radioactive potassium in a banana, but that's just shifting around the radioactive materials already present in the environment.
Wherever you dump the fungus, or the ashes of the fungus, will be more radioactive than before. So a bio-remediation plan would likely grow fungus, separate most of it from the soil, and allow the remaining fraction to regrow, repeating as necessary. The separated fungus would be burned, and any radioactive fractions removed from the exhaust gases and dissolved in liquid or crystallized somehow. The ash would be vitrified into glass pellets.
And then it'd probably still be less radioactive than an asphalt parking lot. But okay, seal it all up inside a drum and forget about it for 10000 years anyway.
Circulate it within a semi-closed system full of funghi. A reverse breeder reactor - a condensing decayer. Vent excess material to radiology equipment.
Then sprinkle in some high-melanin humans, to grow your very own super-mutant facility personel. Perhaps also feed them mushrooms, to speed up the adaptation process.
Uranium -> thorium -> radium -> radon -> ... -> lead is a natural decay chain that does not typically activate other atoms to become unstable, so the decay energy between uranium and lead represents all the radioactivity there will ever be from that uranium. You can't predict exactly when it will be released, and because radon is a gas, you can't as easily predict where it will be released, but once you get to stable lead, it's done.
If you tack up a slab of any stable nucleus higher than iron on the nuclear binding energy curve to the inside walls of a neutron chain-reaction reactor, you can probably get it to absorb neutrons of the appropriate speed and become unstable, promising future radioactivity with an amount of energy between its current state and whatever its final decay product may be. That may be less total energy than the difference between uranium and lead, but it probably runs faster from start to finish than billions of years, and is probably more energy than the absorbed neutron.
So aside from natural reactors, which mostly shut down a long time ago, the only increases in radioactive potential are going to be from human-built reactors. The radon is just moving primordial radioactive potential from where the radium is, which is also where the uranium or thorium is, to wherever heavier-than-air gases can accumulate. If you remove the radium, you stop that. If you encapsulate the radium in a glass that traps gas, you stop that.
Mostly, we don't bother trying to remove trace amounts of uranium and other radioactive isotopes from mineral resources, but if a fungus could do it cheaply, it could make coal ash less dangerous to process and store.
I.e. if you seed radioactive soil with radiotrophic fungi, wait a few years, and then mechanically separate fungus from soil particles, the separated soil would be less radioactive than it had been previously.