It means "mechanically stable", which could be either good or bad depending on the question, but is generally a limited good thing.

At the least, it means these particular compounds aren't quickly breaking down into ever-smaller nano-particles that can be absorbed into living things.

I think they mean that the fuel rods are not breaking down, aka leaching into the environment, as fast. That's a good thing.

For radionuclides more long-livd means less radioactive per unit of time, though. Of course uranium compounds can be toxic in the chemical sense as well, but I’m unsure if uranium compounds make it to the top threats in that list compared to e.g. arsenic and lead.

Of course radioactivity needs to be respected, and the exclusion zone is there for a reason due to factors such as hot spots.