The problem is not hard, I'd even wager to say it's solved. Simply use a lot more filters, basically build big wastewater treatment plants (covered sedimentation tanks, [reverse]osmosis filters, last resort, use closed loops and fractionating columns [like the distillation towers at refineries]), it just takes a lot more energy.

Similarly we can make carbon-neutral concrete and steel, it just takes a lot lot lot more energy.

And we kind of dropped the ball on energy because of costs.

So now we are in a two or more front war for more and clean energy.

I don't know anyone specific, but I've heard about astroid mining as an alternative to mining rare earth metals.