Nuclear waste will outlive everything in the present. Plastics and CO2 are pressing against deep time, but nuclear waste is already there. In as much time as has past in the Holocene, nuclear can laugh that off as a blink of an eye.
Uranium is already there, naturally. Nuclear waste is only uranium/plutonium/whatever, slowly decaying into lead. That's gonna happen regardless.
The only catch is that humans have mined and purified the stuff into dangerous levels of concentration, and for whatever stupid reason, don't seem to have any practical method of recycling the usable nuclear materials from the nuclear waste humans have already made.
Then again, I guess similar can be said about plastics. Why the hell is it that humans can purify raw rocks, dirt and oil into usable stuff, but can't be bothered to recycle/re-process the already previously purified stuff we throw away?
Why can't we just mine our landfills for minerals and materials?