There was a definite missed opportunity to bring Russia into the fold, but I think given the bad blood between the Baltic states/Eastern Europe and Russia, any attempt to bring Russia on board as a partner of NATO would have been met with massive protests and resignations from NATO most likely.
You can't just get rid of 52 years of history in less than a decade.
The expansion of NATO eastward though could have been handled in a more tactful way, less wang-waving at the Russians.

Still, here we are, no going back now, Cold War round 2. :ping:

Joining NATO would certainly help Russian Navy, as it would then be concentrated in one theatre (Pacific) rather than be split between 4 theatres.