It’s my understanding that the US used to claim that it was inappropriate for the State Department to make binding promises that someone would not be sentenced

It’s my understanding that the US used to claim that it was inappropriate for the State Department to make binding promises that someone would not be sentenced to death because the State Department is part of the executive branch and should not interfere with the judicial branch. The US got away with this argument for a long time. Eventually, countries made it clear that the US would have to solve its own separation of powers issues if it hoped to ever get extradition requests approved. This is the diplomatic equivalent of saying “that sounds like a personal problem to me.” The US did eventually find a way to provide those promises without interfering with the courts. Reneging on a promise like that is the kind of thing the US can only do once: sure they would get to execute Assange, but the natural result would be that the UK and other countries would stop extraditing people.