It is not unreasonable to worry about war given the current state of the world. Sometimes I wonder if people who label everything as "unreasonable anxiety" and mental illness are the ones with the mental illness- it is not healthy to lose your preservation instinct to the point that nothing will worry you! There is a reason why any animal, us included, has the fear feature installed! Also, a news source is not unreliable just because they are saying things that make you feel bad!
To the OP: I can't remember where I heard this, but I found it comforting: generally speaking, in life both optimists and pessimists tend to be wrong. Most of the time the medium-bad scenario comes true. Take the pandemic for example. At the beginning, some people were in complete denial that it would be a thing. Others were extremely scared and fearing something on the scale of the Black Death. What happened was, well, serious disruption in society, and the amount of (ongoing) death and illness caused by Covid is not to be minimised, but it was very much a medium-bad scenario rather than an Apocalypse.
It will probably be the same in this case. Most likely, current conflicts will continue to develop and escalate, but things will stop short of global war or nuclear apocalypse. I don't believe the UK will be nuked, but disruptions in supply chains, power, communications are very likely due to cyber attacks, sabotage of underwater infrastructure etc. So instead of worrying, a good way to deal with it would be to prepare for, e.g. a situation where the Internet and/or the banking system are down for several days.