What do you do with the mushrooms afterwards? (In the heavy metal case). Presumably you can't eat them, burn them... Do you just pile them up somewhere?
From watching chemistry videos on YouTube, burning them seems like the way to go. I'm guessing you'd burn them in a purpose-made furnace to melt and concentrate the metals, then put the result into safe storage.
The benefit being that this reduces the energy usage required to fully separate the substances? Otherwise you could just apply this process and cut out the fungus entirely.
By "apply this process", you mean to put the soil or water directly in the furnace? The fungi are performing chemical concentration/separation. Depending on how hot you needed to heat the soil to get meaningful separation, you might end up damaging other properties of the soil by heating it so hot.
With water, it would have to be super contaminated for the majority of the dissolved compounds in the water to be heavy metal compounds, so distilling the water would still leave you with some mixture that you'd probably want to chemically separate. At least you wouldn't be causing any damage to the water by boiling it away, but it would be pretty energy-intensive.