USSR was also once told in ~1990 "no NATO expansion to your doorstep". And now look what happens / has already happened due to Atlanticism pushing its agenda.
The Budapest memorandum however was a written agreement, much more meaningful, though sadly not binding.
[1] https://hls.harvard.edu/today/there-was-no-promise-not-to-en...
No, they weren’t, as even Gorbachev admitted, and even if they had been given private assurance not memorialized in a treaty or even a formal executive agreement, there would be no reasonable expectation of a binding commitment that survived the administrations on each side then in power, much less an actual collapse of the Soviet Union.
It’s not like the Soviet Union didn’t understand the mechanics of how binding international commitments are formed.