My assumption is that they will continue the propaganda campaign they've been doing for at least ten years now; they fuel right-wing political parties that have an insular approach, "eurosceptics", an "own people / own country first" mindset.
look at the US: Trump is Putin's buddy, and he pushed the 'America First' tagline.
Look at the UK, they broke away from the EU.
Look at the eastern countries, Poland and Hungary; they have right-leaning governments that broke the rule of law and the separation of legislative branches, which caused them to get sanctioned by the EU, which fuels anti-EU sentiments. And in eastern Europe, anti-EU is pretty much equivalent to pro-Russia.
I haven't heard about it myself, but I'm sure anti-NATO sentiments will increase as well. It's only a matter of time before they get people to leave NATO. Especially if NATO does not come to the defense of a NATO country, they will lose their trustworthiness then.
While I agree that in Eastern Europe anti-EU often means pro-Russia, Poland is a more of an exception here. Poland still has a very negative aftertaste of Russia after WWII.
But if anything, Eastern European countries will cling to NATO more than ever, they most certainly won't leave it.
Just look at the most recent speech of the Czech president, who is generally pro-Russian (the president, not the whole country). In the speech he absolutely condemned Russia's aggression and expressed support to Ukraine. Moreover, he urged to kick Russian Federation out of the SWIFT system as soon as possible.
look at the US: Trump is Putin's buddy, and he pushed the 'America First' tagline.
Look at the UK, they broke away from the EU.
Look at the eastern countries, Poland and Hungary; they have right-leaning governments that broke the rule of law and the separation of legislative branches, which caused them to get sanctioned by the EU, which fuels anti-EU sentiments. And in eastern Europe, anti-EU is pretty much equivalent to pro-Russia.
I haven't heard about it myself, but I'm sure anti-NATO sentiments will increase as well. It's only a matter of time before they get people to leave NATO. Especially if NATO does not come to the defense of a NATO country, they will lose their trustworthiness then.