Prussia stopped being Britain's sword after the seven years war and would happily traded them for Russian backing with the right incentive and the Russians could offer the right incentive and is common touted has having the best and largest army at the time, should the Prussians win a war against Austria and Briatin they stand to gain not only Saxony but Hanover and likely the Rhineland they got otl, while they stand to lose maybe Silesia, easily worth the risk.Prussia was British sword on continent against Russia and France, now that "sword" fights against Britain on Russian side, so either they will switch sides before it's to late or they are gone.