This promise is a myth [1]. At best, it was an informal statement by some guy in the U.S. government [2]. This has been blown out of proportion beyond any semblance to reality by Putin's propaganda.
And if it had happened, it would have been an agreement with the Soviet Union. Which does not exist. Russia, in 1994, formally agreed to "respect...Ukrainian independence and sovereignty in the existing borders" and "refrain from the threat or the use of force against...Ukraine," among other things. It has flagrantly broken these agreements.
[1] https://www.brookings.edu/blog/up-front/2014/11/06/did-nato-...
[2] https://link.springer.com/article/10.1057%2Fs41311-020-00224...