Before Russia did their heel turn in the aughts, they almost joined NATO after a period of significant cooperation. Russia seeing the U.S., or it’s allies, as enemies is a symptom of Putin turning a fledgling democracy into a dictatorship, not the natural state of affairs.
Go to the “Development of post-Cold War cooperation (1990–2004)” section and check out “NATO-Russia Founding Act”, “NATO-Russia Permanent Joint Council”, and “NATO-Russia Council”.
Back then the talk was pearl clutching over NATO with Russia being seen as some racist white alliance against China, MENA, India, and others in the global south.
Russia only sees us as enemies because Putin needed to create enemies to seize and consolidate power.