I do not think that would really work either. It would be suicidal for either EU or Russia to fight each other. All this "threat" talk I think is just a way to squeeze the money and governments always need some enemy to deflect attention from their own fuck-ups.
That could be true, it might be more theatre than threat.
I only know that anytime the US reduces (or Russia increases) the military presence in some area, it's in the news for weeks (as examples, Turkey, Syria, Estonia, Germany come to mind).
Also, the "theatre" can also work, as politicians want to be re-elected and if enough people believe that their country is in risk because the US troop numbers are reduced, then it becomes a way to pressure the EU even if the real military threat is not that great.
Though I still think my point stands, as the US must have ways to pressure the EU to not take a strong stand against tech giants.
Of course the US can and will pressure. But up to a point. Otherwise they might be told to f.. off and mind their own business. More likely is that they will reach some compromise.
What's the point? You think the US will really threaten EU with the war?