Additionally, Germany is one of the biggest contributors in NATO and also one of the stability anchors in the EU. Another one would be France, the third one was originally UK.

With UK gone, thanks to Brexit (which was also highly boosted through Russian aid in propaganda spreading), it's only France and Germany who hold everything together.

Italy and Austria are already in the hands of the far right, Le Pen in France is getting stronger - if they get strong enough, they'll defeat their land and the EU from the inside.

Putin knows very well a modern war against the EU can't be fought with conventional weapons. Ukraine has proven how expensive that is. And there isn't even a nuclear threat that would arise if he ever openly attached the EU. Therefore Russia fights undercover - through propaganda, through espionage and by manipulating the politics of the countries they seek to defeat. And if we look at the current standings, this war is running almost according to plan

This isn't even limited to the Ukraine war. Russia's geopolitical strategy since at least when Putin got in charge was to sow chaos through undermining the democratic systems of their enemies. Right-wing extremists generally are very good at destroying democratic systems if they get in charge. So it's really no surprise that Putin has no problem helping such parties.