There is a lot I disagree with in your post but I will focus on two things:

Britain “declaring war”- no they won’t. War is a legal concept and is quite outdated, very different to the common use of the word. America, for all its conflicts, has only been “at war” 5 times in its history. For the UK, things like the Falklands war or the Iraq war were not “actual” wars. No one declares war these days. Neither the US or UK have declared war since World War 2. It just isn’t necessary, and it boxes in your options. Because a war can only end by armistice or surrender by one side. So Britain won’t declare war, even if Putin attacked a NATO country, NATO would respond but it’s still very unlikely for war to be declared.

Secondly, the use of Nuclear weapons was absolutely about saving lives- US servicemen’s lives. The invasion of Japan would have required 500,000 soldiers minimum according to projections at the time, and have 100,000 casualties minimum also. America did not want to commit to that.

But, unlike the popular myth, the nuclear bombs did not stop WW2. Reports from Japanese command were they were unfazed by the nuclear attack, which makes sense since they were unfazed by the mass firebombing of Tokyo prior too. So why did the Japanese surrender? At the very same time as the nuke droppings, 1 million Soviet soldiers invaded Manchuria and charged towards Japan. Unlike the Americans, the Soviets were not afraid of horrific losses and within days the Soviets had already invaded some of the islands of Japan. That’s what got the Japanese to surrender.

The Soviet assistance is forgotten in the pacific just as American Lend Lease assistance is forgotten in Russia against Germany.