I’m not buying that “both sides” want another round of fighting. The US definitely does - it’s their go-to mode anyway, and they’re checkmate on all other options. Already the rest of the world has decided they’ve definitively lost this war, so only starting another fight will make it look as if the war’s still on and the jury’s still out. It won’t make them win, it’ll just be damage control.
Meanwhile, Iran won’t be interested in more fighting if they don’t have to. Time’s on their side: every day that goes by with a choked strait of Hormuz, the more the world economy will slide and literally the whole globe will blame Trump and his feckless minions. They’ll obviously respond to an attack, and they’ll threaten hell as a deterrent. But why fight when the economy will do the job for you, and your enemy will look like the fool he is?