I've heard multiple times that Russia has nuclear subs in the ocean off the East Coast of the US and if a nuclear exchange were to eventuate, their sub-launched missiles would hit rather rapidly.  And that the US has similar close-range strike capability from Europe.

My point was that we have been silently in close strike range for decades(?) and this has been normalized. Back in the "Cuban Missile Crisis" such close strike range was very worrying to Americans who didn't know it was mutual and Kennedy secretly made a deal to pull our missles out of Italy and Turkey.  But even at that time, it wasn't a real "crisis" because it was mutual and so neither side could win, and neither side was going to push the button.

Russia being at Cuba today doesn't present much extra threat of a nuclear exchange. The US intel agencies have already publicly said there are no nuclear weapons on those Russian ships.  What it does present is a conventional attack platform with Kinzhal and other hypersonics.  It is meant as a warning, since the US keeps crossing red lines:  "cross another red line attacking Russia with your missile systems and perhaps we will attack the continential USA with our missile systems... we are serious, stop pushing us."  It is meant to stop the escalation cycle.  "Escalate to deescalate".  But of course every escalation could provoke more escalation in retaliation instead.