Prof. Jeffrey Sachs of Columbia University gave an interview to Tucker Carlson recently, in which he stated (25:45 into the interview):
The US had promised, unequivocally, to the Soviet Union, in the context of German unification, as of February 1990, that NATO would not move one inch eastward.
But how could such a promise be given without a vote in Congress?
Even an act of Congress or a treaty with Russia can't guarantee that NATO will not be expanded.
Any law that Congress passes and is signed into law can be later undone by a future law that Congress passes and is also signed into law.
Regarding a treaty, any that is entered into can later be made null if they choose to leave it.
[Completely ignoring your example and just answering the general question]
Now, a lot of countries and negotiations come to terms & treaties that technically need internal (re-)approval, this is common practice.
Why does it (usually) work? Because even moderately opposed politicians value the international integrity of their promises over minor disagreements, so this kind of promises/treaties has an incredibly high chance of passing. Additionally, any skilled negotiator or official will of course only promise what they know has a decent chance of getting passed.
This however requires a political system and landscape that cares in some way about it's international reputation, which is why a breaking of such promises pretty much always falls into 4 categories:
Since all of those are easy to ascertain, it's upon the "receiving" nation to determine the validity and value of such promises, aka how much it can rely on these words. The important part is that it doesn't matter whether the internal approval happens or not, any of these criteria can lead to promises/treaties being broken anyway. Depending on the signer and point in time, a signed treaty can be as valuable as a ratified one and a ratified one can be as worthless as a post meal napkin. One additional factor is the international community whose pressure can elevate the value of a signature far above the ratification itself (or the other way around if major powers oppose the treaty signed/ratified).
Option B: Lying
You can make all kinds of promises if you absolutely don't care (see category 1 in the list above)
You're illustrating the problem: the US can't make a legally binding promise without a vote in congress. But Gorbachev apparently opted to trust Western leaders anyway.
Compare: suppose your roommate tries to borrow your car. You ask them what happens if they crash the car, and they say they'll pay for the repairs. You agree to lend them your car, and they crash it. Afterwards when you call them for payment, they say "We never signed a contract. I have no obligation to pay."
Legally it's possible their argument might hold water. In practice they'll cease to be your friend, regardless of what the legal result is. That's a close parallel to NATO expansion: it is why some people think Gorbachev's big mistake was not to get the promise in writing.
