As early as January, the NYT was reporting that Ukraine was deploying additional troops to the region due to its strategic location:
[T]he shortest route from Russia to Ukraine’s capital, Kyiv, is from
the north. And it passes through the isolated zone around the
Chernobyl power plant, where the meltdown of a reactor in 1986 caused
the worst nuclear disaster in history.
In one of the incongruities of
war, that makes Chernobyl an area that Ukraine thinks it needs to
defend, forcing its military to deploy security forces into the eerie
and still radioactive forest, where they carry both weapons and
equipment to detect radiation exposure.
In addition to sitting in the middle of the shortest route to Kyiv, it also holds a river crossing.
After reports of clashes at the site, this question was put to Dr Jack Watling, a research fellow for land warfare at the Royal United Services Institute on BBC Radio 4’s PM program at around 17:39:-
Interviewer: In the last few minutes it’s been reported that the Chernobyl power
plant, captured by Russian forces, I don’t understand - it’s not a
working power plant is it? Or, what would be the point of getting the
Chernobyl power plant - but it does seem something has been going on
there this afternoon.
Watling: I mean it’s fairly standard practice that if you’re taking over a
country you take over all the critical national infrastructure, and
Chernobyl has both symbolic relevance but also you can start playing
dirty tricks in terms of, you know, claiming that, I don’t know, the
Ukrainians are conducting artillery against it and these kind of
things. So you know, you want to seize areas that are symbolically
valuable and areas that are valuable from a services point of view,
and the Russians will try and do that.
Radio Free Europe, meanwhile, cites an unnamed Russian security source, saying that “Russia wants to control the Chernobyl nuclear reactor to signal to NATO not to interfere militarily”. They also quote Deputy Interior Minister Anton Heraschenko acknowledging the devastation that could occur if the site is damaged:
If as a result of the occupiers' artillery strikes the nuclear waste
storage facility is destroyed, the radioactive dust may cover the
territories of Ukraine, Belarus and the EU countries
This suggests that the site may have strategic relevance as a forward base that Ukrainian troops dare not attack with artillery fire.