Fyi: The EU is 20 years old and police isn't in the defense budget. A budget 4 times as large makes a way bigger army.
The USSR military wise, was 5 times as strong and still they collapsed. The Russian economy isn't strong enough to support a war this size in modern times and in the process losing their primary trade partner. The EU can easily spend more on financing a war than Russia, military spending is currently < 2%.
What you mean by fragmented is actually being solved by Russian threats through joint exercises.
A fragmented army ( multiple countries with different strategies) actually won in the past ( WW 2), so history doesn't seem to agree.
You are also forgetting that attacking 1 country is now attacking a continent. You don't know what the response will be or where the threat will come from. The EU also has a lot of allies because of its economic power.
While Russia would send it's army to the Western border, some other Asian countries with approval of the West ( and because they are under attack) would have no trouble seizing Russian land. I'm pretty sure that China would be quick to grab some too ( is the easiest quick win ever for them) and Russia wouldn't be able to stop them. Since their army would be in the West and immobile. Leaving the East open without much resistance or their army fragmented.
Multiple countries ( eg. Poland for one) are already on high alert because of Russian threats.
The power would actually be fragmentation. Russia is just one railroad to slow it's tanks ( transportation). European countries are only unsafe at the border of Russia and perhaps Turkey.
Russia is one HQ ( Moscow) within 80 km from the European border, we have never been this close.
I'm saying that if Russia would actually attack the EU ( which would be incredibly dumb). Russian infrastructure would be easily wiped out and their economy would probably collapse again.
They would also lose a lot of land in the East.
Since 47% of their trade is with the EU, it would cause further "unrest" among Russian population. Nobody would benefit.
Facts differ from propaganda.
I don't even think that actual war with 2 similar countries is possible anymore. The countries that are the most scared for actual war are the ones that censor things.
Eg. Unrest in China about pork prices.
Oh yeah, I forgot nuclear arms. Which would make an actual war very risky. Even with the EU's technical and numerical advantage ;)