It’s my understanding most “nuclear waste” is “stuff that has some residual radiation from being inside the radioactive area of a nuclear power plant” like machinery and general trash. In addition, radioactive water can be cleaned up enough to reuse in the steam cycle, and then you just have to get rid of the fairly radioactive resin once it’s spent.

And before someone asks, no, the water some plants have coming out of their cooling towers is not that radioactive water, it’s a separate loop of water that is used to cool the primary loop.