The NATO Expansion line has been disproven to death.
Putin sees the fall of the USSR as a historical wrong that must be righted. He uses NATO Expansion as an easy excuse to sell to the rubes, but it's just that, an excuse.
He was going to go after Ukraine and Georgia NATO or not.
It hasnt been disproven even once. The usual attempts to do so deny geopolitical realities (e.g. assuming the Finland-Russia border is as vulnerable as the Ukraine border).
Georgia was, obviously, left alone after it dropped its NATO ambitions, disproving the rather quaint theory that Putin is intent on reforming the USSR.