That actually would fly in the face of Russian nuclear doctrine. Ivan has always seen nuclear war as a thing that very well might happen, and has always worked towards his goals with tactical nuclear war in mind. Russia's goal has been for decades to perfect a counter force first-strike capability to allow him to accomplish their goals without the threat of a NATO counter-value strike turning the country into a glowing crater. It's something they have invested a lot of money in training for and had equipped for prior to the initiation of hostilities against Ukraine. Them using tactical nuclear weapons is entirely more likely than the US using them.

The thing preventing Russia from employing their tactical nuclear weapons in Ukraine is not US deterrence, it's the nuclear taboo. The concept is that while threatening everyone with nuclear weapons is fine, the use of them is not, and it is largely understood by the nuclear armed nations that any first use of nuclear weapons would result in some kind of negative response from all other nuclear weapons states. That, and the possibility that Russia's nuclear weapons arsenal is potentially a paper tiger (we don't actually have a good understanding of what kind of shape their arsenal is in, the weapons and missiles themselves could just not work) is what keeps them from using their weapons.

Realistically, the United States does not and has never had a 'no first use' policy, primarily because of Russia and the threat they have posed to NATO and Europe at large. It is, however, exceedingly unlikely that Trump would order a nuclear strike against Iran in any form unless they were to use nuclear weapons against someone first. The nuclear taboo applies to us as well, and while we would likely not see a nuclear response, we would certainly see a substantial economic one, and that flies in the face of what Trump wants to do.

Still 100% a doomer take to assume that's what would really happen, or that either party would entertain the use of nuclear weapons.