> Whereas Japan would’ve continued the war and brought it back to the US mainland eventually.

This is simply ahistoric.

Japan was on the brink of loss and everyone knew it (including the entire Japanese chain of command), the main sticking point was the conditions of surrender and the Japanese were deluded (partially by the US, intentionally or not) into thinking Russia could get them more favourable surrender conditions. These delays, combined with what seems to be at least some wish to show America's might, lead to the bombings.

No reputable historian would make the argument that in 1945 it was remotely likely that Japan would not lose the war irrespective of the bomb, let alone Japan actually invading the US. If the US had explicitly stated they would not try the royal family for war crimes and keep the 帝 (emperor) alive, Japan would've surrendered (this is literally the only important condition they wanted, and it's what the US was planning on doing anyway).

If you'd like to watch a very long video explaining the events leading up to the bombings with a very detailed timeline: https://youtu.be/RCRTgtpC-Go

The WW2 nuclear bombings of Hiroshima and Nagasaki predate any real nuclear doctrine. I don't think they are particularly informative of nuclear doctrine today. And yes, as the other poster says, Japanese invasion of the continental US is an absurdly unrealistic proposition - even if Japan had achieved all of its wartime objectives.