> Nuclear waste in contrast is literally just barrels/boxes of stuff. You can pick it up with a forklift and put it inside a sealed container for the next thousand years.

You can't pick it up with a forklift to put it inside the sealed container. That would make the forklift (and its operator) radioactive. You can only use a forklift after it's already within the sealed container. See for instance this real-life video (shot on a nuclear power station in my country), which shows used nuclear fuel rods being put inside a sealed container for long-term storage: https://www.youtube.com/watch?v=7X5K46ALdD0