This ranks way down the list as yet when it comes to possible nuclear/WW3 scares.
The 1961 Berlin crisis where US tanks faced down Soviet tanks in a standoff in Berlin at checkpoint charlie until both Kennedy and Kruschev both went oh sh!t! And both basically agreed to move back one meter if the other did and so forth.
The Cuban missile crisis as others have given insight into.
Operation Able Archer 83- where NATO was conducting war games over Europe that would escalate to a nuclear strike. The Soviets distrust lead to them arming and loading nuclear weapons onto planes all over Eastern Europe and East Germany. The Soviets thought the exercise was a ruse for an actual nuclear first strike due to the realism of the operation.
The 1983 false alarm incident- when Russian early warning systems picked up 5 ICBM launches from the US. Only for the operator in the USSR not reporting it up the chain of command as he didn't believe it could be possible that the US would and waited for more evidence.
So as of right now, the Russia-ukraine conflict is down the list but as we know, theres potential for escalation.