Keep in mind that there has, of yet, been no actual nuclear incidents connected with the Ukraine war, only threats. Just like with nuclear weapons, nobody wants to open the Pandora's box of turning nuclear plants into military targets, because that may very well backfire on them. Russia has its own nuclear plants that it doesn't want to see sabotaged either. This doesn't mean it won't happen, of course, but the risk is much lower than you present it to be.

Besides, in a thousand years it is very likely that we will have much better technology for containing and cleaning up radioactive fallout than we do now - and what we have now is already miles ahead of what we had during Chernobyl, as was made apparent during the Fukushima incident.