> 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
You park the forklift in the storage container and seal it in. It's not that hard.
Anyway, the forklift example wasn't about literally picking up pieces nuclear fuel with a forklift. You obviously use the forklift to move the shielded container around which contains the nuclear waste. Nuclear fuel in general is always at least in a water bath, which shields the neutrons, so your forklift is going to be fine.
In contrast to nuclar fuel, you cannot use a forklift (or any other equipment) to feasibly pick out the evenly mixed mercury atoms from the ocean or the atmosphere that we put there from burning coal.