This is just posturing of the like that we’ve seen since I’ve been aware of world politics, in the 80s. Before then too, but I only have read about that.
There is a line, but given nuclear war is unprecedented, I don’t know where that is. That said, if we are talking nuclear weapons, I don’t think anywhere is safe.
When I saw that headline, I assumed that there were already nuclear-armed subs in the relevant areas, because the entire point of those subs is to always be in position to retaliate to an attack. That would imply that the media announcement that Trump had deployed those subs was entirely performative; any such order would simply involve telling the relevant subs to keep doing what they were already doing. So, the headline would be technically true, but in practice a no-op, and therefore perfectly suited to feed the media without accidentally signalling anything substantive to anyone who knows how things actually work. Epistemic status: best guess on my world model, but not an area I've paid much attention to.
Part of what the question is asking is how do we know (decide?) the difference between performative and true existential threat.
Recall how Putin has been "putting nuclear forces on high alert" over and over and over again since the start of the war, including during the initial events in February 2022. It never meant anything.
I expect this is the exact same thing. Trump is just joining in on the posturing fun, because he's Putin-like in this regard. I feel fairly confident that neither Putin nor Trump will ever actually nuke over this conflict in its current shape, and you should feel free to ignore all of their nonsense.
Some context here: I'm Russian and I pay some attention to Russian anti-Putin political analysts. I haven't gone in-depth on verifying their analyses, and there are obviously some biases there, but they offer a compelling perspective which I think is missing from Western views.
Western Kremlinologists, from what I've read, tend to take Putin's government seriously. They effectively steelman his decision-making. They try to figure out how various actions Russia takes may be in Russia's geopolitical interests, they're making predictions based on the expectation that Russia is going to act to advance those interests in the future, they talk about things as if the Russian government would make hard choices to protect said interests, et cetera. Whenever Russia does something stupid, they try to infer flaws in Putin's model of the world under which those actions make geopolitical sense, rather than assuming he did something geopolitically incoherent.
The perspective among Russian anti-Putin analysts is that the above is mostly false. Russia is not well-modeled as a serious-minded geopolitical agent. Russia's government is under Putin's near-total control (especially after the latest purges), and Putin has no priorities higher than holding onto his power and entertaining himself. He doesn't view himself as an extension of the Russian state whose interests he ultimately (or at least partially) pursues, there are no other factions with explicit decision-making power who can steer Russia's actions away from whatever catches Putin's fancy, and the processes that fueled Putin's rise to power were not processes that shaped him into a geopolitics-minded actor.
Russian opposition often describes the current state of affairs as Russia being controlled by an organized crime group, with Putin the kingpin. This might indeed be a better model, rather than viewing them as a more traditional autocracy.
Putin does like empire-building, and having power, and when other world leaders bow down to him and attempt to placate him. Inasmuch as those goals are aligned with Russia's geopolitical interests, Putin will pursue those interests. But only by coincidence. If some decision would hurt Putin's power or ego, he's never going to do it, no matter how much it would be in Russia's interests.
For example: Ending the war. Does the war threaten to crash Russia's economy? Does it make Russia fatally dependent on the whims of e. g. China? Sure. But ending the war is guaranteed to return home a ton of disaffected people with combat experience, and turn the world's spotlights away from Putin. That threatens his power and fun, so he won't do it, no matter how good of a deal he is offered. (And I'm given to understand Trump was offering quite a good deal.) He didn't expect Ukraine to turn out the way it did (it was probably intended as a Short Victorious War to boost ratings at home in advance of the 2024 elections[1]); but now that he's settled into it, he does not want an exit strategy.
Similarly, threatening to nuke is a pretty good action, by Putin's utility function. It freaks the Western politicians out, they start calling him attempting to placate him, great time is had.
But actually nuking, especially someone who may nuke back? Hell no. That might lead to Putin's death. He will never do it. (I guess one exception may be a situation where he thinks he'll be killed anyway, e. g., if there's an actual march-on-Moscow ground invasion of Russia. But maybe not even then. Edit: A plausible alternate outcome is that he'll flee to a hidden bunker somewhere and attempt to harness every resource at his disposal to stall/wait it out, hoping the situation would somehow eventually progress in some way that gives him the opportunity to recover. "Stall for opportunity" seems to be his go-to strategy.)
And Trump proactively escalating to a nuclear exchange from his end seems even less likely.
Again, I'm not confident this model is correct, I haven't ran comparative analyses of this vs. take-Russia-seriously Western models. But it seems solid to me, and is more postdictive of e. g. how rotten Russia's industrial-military complex turned out to actually be.
Russian elections are not real, but: (1) the election days can serve as Schelling points for public discontent which may be harnessed by defecting elites in an attempt to depose Putin, (2) the Simulacrum Level 3 appearance of having the mandate still needs to be maintained. So it still makes sense to prepare for them.
I notice the headline “Trump deploys nuclear submarines” and my first instinct is I need to grab my siblings, parents and whatever friends and cousins are willing to listen and run to the old country (which has little to no chance of nuclear attack). Am I overreacting? Where’s the threshold for such measures? What would it take to convince you that where you lived was no longer safe?
(The underlying logic is that if the US takes actions to threaten a nuclear power, the US would be vulnerable to nuclear retaliation).