But the idea I’m proposing isn’t to integrate everything into the budeswehr. Also Russia could be seen as a threat to EU countries depending on who signed up. Enemies are never constant, the army would be there to defend in case we needed it.
But your idea is not what's currently happening. It's all based on integration with the Bundeswehr, a military with only four working Eurofighters, 0 working submarines or A400M transport planes, 95 operational tanks (out of c.300) and god knows what else. It has never once been deployed in serious strength abroad.
Post-Brexit, the only EU military power that could carry out the task is France but it has serious reservations about doing do so. Plus Germany is unwilling to give up political control over its glorified town militia. I doubt Eastern Europe is willing to trust Brussels with its defence either and will stick with the Americans for the foreseeable future.
Oh, and then there's language barriers which make it difficult in practical terms unless they ironically make them all communicate in English (good luck persuading the French to do that).