An agreement was made. It was not codified in a treaty, yet judging from the context (allowing Germany to be reunified), it would have been an essential requirement for Russia to have that assurance.

We can criticise Russia for not having demanded a written agreement, which they likely didn't get because they were weakened at the time, yet it doesn't change the circumstances either way.

I don't condone Russia's actions by recognising the argument that NATO is a threat to them, at least from their perspective.

Noam Chomsky articulates it well in this short clip: https://youtu.be/Iq5IlDB-Ago?t=187