I have heard from multiple cold war scholars some that were in government at that time that they promised this to Gorbachev. That said, it was never formally ratified.
This is just one example, another one is the non-adjustment of borders without agreemnt. But this was broken in the 90s when the US created Kosvo.
The missile treaties were broken by Bush.
> The end of Cold War was USSR unilaterally dissolving
Arguably the Cold War ended with the treaties between the Soviet Union and the US before it devolved. That is at least what US negotiators believed and you can listen interviews with them.
They are actually quite angry that people now say that the cold war ended because the Soviet Union collapsed.
> Furthermore, Yeltsin publicly said that eastern europe can join NATO if they wish.
Yeltsin was weak and had to agree to a lot of stuff that he didn't like. The Russian elites certainty never wanted the NATO to expand east.
> As an ex-USSR citizen, Russia was damn friendly in early 90s.
They are incredibly friendly right at the point in the history where they are weakest. Lenin was so friendly he signed over half of European Russia.