If I remember well most radioactive waste by volume is not from nuclear energy production and the share that is very small would be drastically lower if places like the US didn't ban it's recycling. It's half life can also be drastically reduced.

I also wonder. Is it the implied danger over those tens of thousands of years or would it end up being something more similar to Ramsar in Iran long before that?

You simply put waste deep underground in geologically stable rock. https://en.wikipedia.org/wiki/Onkalo_spent_nuclear_fuel_repo...