The US is under no obligation to start a global nuclear war over a tactical nuke in Mariupol.
I also don’t think that will happen.
I also don’t think that will happen.
Correct.
But, once you start using tactical nukes (or the threat thereof) to gain territory, where does it stop?
I think it only stops when every country has their own tactical nukes to retaliate with.
FWIW, here's an interesting presentation by Col Sam Gardner (USAF RET) who taught strategy at the National War College, Naval War College and Air War College. It's a possible use of Russian tactical nukes in Ukraine, and how to respond.