Building a nuclear weapon that can be carried by Iraq's missiles is relatively difficult, because miniaturizing nuclear weapons requires much more complex designs. It took the US and the USSR quite a few test explosions to achieve such a warhead.

Building a bulky nuclear weapon that fits in, say, a shipping container, is not hard if sufficient highly enriched uranium is available. That's Hiroshima level nuclear technology, the gun-type bomb.[1]

This is the difference between the "years away" and the "weeks away" estimates. Depends on whether the the delivery method is an ICBM or a shipping container.

[1] https://en.wikipedia.org/wiki/Gun-type_fission_weapon

For various reasons I'm inclined to agree that Iran likely doesn't have much of a nuclear weapons program beyond enrichment.

That doesn't mean that they lack plans or means to advance one, and they certainly have the talent.

As for US intelligence agencies, it's worth being reminded they've let slip nuclear weapons development programs before: https://www.everycrsreport.com/reports/98-672.html

To be 100% fair to the GP: indeed, Iran does not currently have an active weapons program. But they do have a weapons program, but they used it so far more for leverage. The truth is nobody really knows what they would have done had they achieved the status of nuclear armed power. But given that even the mullahs understand that there is a bit of a difference between threatening to annihilate Israel and actually doing so with all of the consequences attached to that I think they would be more like Kim or Putin than say the UK or France. They would use it for even more leverage and as insurance against being attacked.

Either way: the US is quick to say who can and who can not have nuclear weapons, but at the same time the US is the only country that ever did use them and it is one of very few countries that has (implicitly) threatened their use in recent memory. The only other two countries to do so are Israel and Russia.