Sadly nukes are not exactly all that complicated to build. The hard part is making the uranium and designing it the first time. Once you know how and have the stuff to make it it's pretty easy to just pump them out. That's why we've got so many of the damn things.

the US and russia had mutual checks in place before the war escalated. so it's very likely that at least a decent number are working well enough

1. The US does not actually dislike the "oil crisis" the US oil companies were in deep debt prior to the Iran war and were barely breaking even on their oil. This was has been a massive windfall for them. It's a political problem for Trump yes, but the actual power players in the US (rich) love it.
2. A tactical nuke on Kiev would not destroy the value of Ukraine. You are too Fallout brained. Look at Hiroshima and Nagasaki. They're perfectly normal cities today.

"on launch" is for specific ICBM systems we know have nuclear warheads in them and monitor by satelite. That is not what would be used here. Automated systems cannot tell the difference between a bomber carrying a nuke and one carrying a conventional warhead. They cannot tell the difference between a normal ballistic missile and one carrying a small nuke. Until it goes off and people notice. There is no automated counter launch for that scenario as we would not even know its a nuke until it goes off. And if it already went off we clearly know where it was going. Iran, Ukraine, Russia, and the US launch missles at eachother constantly. All they need to do is stick a nuke in one of them.

That's only for ICBMs. Nukes could be delivered by plane or cruise missile that don't have the uncertainty related to destination. They would most likely be indistinguishable from a conventional warhead until they detonate.

We got the drone distributor over here.