W-54 isn't here anymore. So instead US have tuned down W-76 into 5-8kt. I.e. getting new capabilities without testing (there are recent tuned down, though not that low, versions of B61 too). And that is open information. One can expect that classified would be at least a step ahead, i.e. something like 1kt. Coupled with high precision delivery and earth-penetration designs (that US has been using across the range - from conventional to B61) that makes for extremely effective deterrence as it allows to take out a dictator like Putin deep in his underground bunker if he crosses the line (Putin becoming the first and primary target himself is the cornerstone of the current deterrence architecture), and other strategic keypoints without initiating full scale war.

I have no inside knowledge whatsoever but we can all rest assured that each side is in a near constant back and forth of implicit unstated "communication" about capabilities and doctrine.

Merely publishing a paper on a certain subtopic in the fusion space can easily be interpreted as an implied threat or threat response.

Of course the US does have a stated doctrine of using nukes only in response to nukes used against it or its allies. It is enormously doubtful that the US would trigger an end-of-days scenario in response to Russia using tactical/low-yield nukes against a non-US-ally like Ukraine, but the uncertainty is for sure purposefully cultivated.

Correct, this has not happened and will *not* happen

One kind of the low yield weapons is to have very precisely placed smaller explosion - those ones is mostly fission core, and the other is to have high neutron flux with minimal blast effects - with that instead of a point you'd want to cover a wide area.