But let’s ask this question. Of the nuclear-armed countries in the world today, which seem the most likely to actually use them in the near future?

Israel is definitely on my short list. As is the USA. Plus a couple others.

As an aside, the entire list is only a short list. There's only nine nuclear states. If I had to list them in order of who is most likely to use them in the near future, Israel and the U.S. wouldn't be towards the top. Here would be the ranking:

Russia
India/Pakistan
North Korea
Israel
China
USA
France/UK

All of these states are very very unlikely to use nukes, because they are mostly useful as deterrents and they are very effective deterrents. But that's my list.

Russia tops the list because they're involved in a hot ground war right now. India and Pakistan are the only two non-allied nuclear states that border each other, and they have non-trivial conflicts between them - including disputed territory. North Korea slots in after that because they are the least predictable, least integrated into the world system - the main deterrent to using a nuke is that it's global anathema, and they're the least affected by that because they're already anathema. Then Israel, kind of by default - they're in a conflict-ridden part of the world, but they have such conventional military superiority and none of their neighbors are nuclear powers. China and the US as kind of a toss up, with the US falling below China because we've got the stronger conventional force and a bit more structural elements in our government that divide power and raise the stakes for a President calling a nuclear strike. And then France and the UK.