I don't buy that argument at all.
Under Yeltsin, Russia was transitioning from a Communist country to a more free market economy and it was chaotic. That was the junction they had arrived at and there presented the opportunity for a very different relationship with the West.
Putin had other ideas - the coercive take over of parts of Georgia, the massacre of 33,000 Chechyn's, the annexation of many former soviet territories, the dictatorial nature of his relationship with many of those countries etc.
Putin has long fought a hybrid war to push his expansionism - through propaganda and military force. One could argue that the 'sphere of influence' is far greater than the old USSR: Syria, Iran and other middle eastern countries, many countries in Africa and an unholy alliance with Xi Xing Ping, India and NK.
The propaganda is endemic in the current French political climate with 2 right wing parties topping the polls and both figures are pro Putin. Putin has his tentacles in US politics. He has tentacles in British politicks. Boris Johnson and others attended parties thrown by the Russians - it was common. Putin has spent his 3 decades in power compiling Kompromat on the back of the parties riddled with prostitution.
The notion of NATO encroachment in menacing fashion is Putin propaganda. Putin has never (bar the odd recent drone and a couple of commercial airline strikes), attacked a NATO country by conventional force directly.
NATO has had every reason to add member states.
It's a bit like saying that you caused the bully to be what he is because you didn't allow the bully to be what he wanted to be. It's tautologistic.
Putin is amongst the more intelligent dictators but the playbook is the same - divert blame, divert attention, claim everything you do is for the benefit of the people and in his case, blame your expansionist actions on forces out with your control, ramp up the threat of those external forces and this justifies your actions. Volume 2 of the playbook is surround yourself with the forces and the finances to carry out your desires and in the process, line the pockets of the immediate thereby guaranteeing loyalty, ensuring control of communication which supports all aspects of the desire for more power and more income. This system of governance is an egotistical and self serving loop. which cannot be blamed on NATO.
Sorry, long post.