I don't think this site is a good place to look for reassurance about this sort of thing OP. It's full of extremely anxious people who catastrophise a lot, and (I can only assume) find some comfort and level of control in calling other people naive and ignorant if they don't also jump to the worst case scenario immediately, however unlikely it may be in reality. There were numerous threads during the earlier stages of covid for example asking whether the virus was literally going to bring about the end of humanity, some of them running for pages and pages, even though anyone who knows a basic amount about biology could say with virtual certainty that that was never even a remote possibility.
Certain parts of other big social media sites like Twitter and Reddit are just as bad. As recently as a few months ago there were posts on Reddit with thousands of comments about how Omicron was going to be the final nail in the coffin of western civilisation etc, and insulting anyone who suggested that total societal collapse due to covid was extremely unlikely, even though we already knew it was causing proportionally far fewer hospitalisations and deaths than previous waves. I would avoid all of those parts of the internet as far as you can at the moment - your anxious brain will latch onto that 'nuclear bombs, end of the world' type of sentiment, even if your rational brain knows those people are no more intelligent or informed than anyone else.
Russia has had nuclear weapons for decades (including, as others have pointed out, in far more knife-edge situations than this). Putin has been president since 2012, and prior to that he was Prime Minister since before 2000. If he was a madman hellbent on a first strike missile launch for no particular reason, he could have done it years ago without any need to invade Ukraine on a BS pretense first. If he didn't give a damn about the consequences to his own country he could have started warmongering back when Trump was in charge and God only knew the outcome.
Instead, his government has been meddling in Western affairs for years trying to undermine the integrity of European and US leadership, and
now he's chosen to launch this attack when the western powers have been further weakened by covid, and when the White House is no longer occupied by a lunatic with a hair trigger. He's attacked a non-EU, non-NATO member state that other major powers aren't obliged to defend and that Russia was already at war with, and there's currently no intention by any other countries to escalate the situation by involving themselves directly in the fighting. He might be an evil man who doesn't care about civillian lives in Ukraine or the lives of his own young soldiers, he might even be genuinely paranoid about this fantasy of attempted Western incursion into Russia like he claims, but none of this seems like the strategy of a comic book villain who just wants to take the rest of the world down no matter the cost to himself. It fits much more with someone seizing an opportunity to get what he wants at a time when he's fairly sure the (military) opposition from the international community will be minimal.
It's a horrific situation for the people in Ukraine and those who have friends and family there, and I'll admit I cried seeing the pictures of people trying to flee Kyiv this morning even though I'm usually not deeply affected by events elsewhere in the world. It must also be a frightening time for many of their neighbours who border Russia, wondering if they're going to be the next target. And I think all of us who are aware of the situation will be unsettled and anxious at the prospect of a bloody war in an otherwise peaceful and democratic European country, even one that's a long way away, because it's not something we're used to seeing - especially coming off the back of two years of other scary and unforeseen events. But I still believe the chances of ordinary British people getting directly caught up in military conflict are very, very, very low.
What I would do OP is try to focus on mitigating the risks that are actually likely and that you can control to some extent. Withdraw cash and keep some of it on you when you go out, so that if any cyberattacks disrupt electronic payment systems you won't end up stranded or low on groceries. If you're able, watch your spending and try to save some money so that you have a buffer when energy prices go up. Then do all the nice things you've already mentioned, like going for walks and having a bath, and focus on your own family's day to day life. Once the situation is no longer changing so rapidly and dominating all social media and news headlines, you'll soon find yourself worrying about normal everyday concerns again! 