The Prussia-Denmark War led to the collapse of the Vienna System, resulting in discord among many small European states. Without the protection of this system, everyone would have to return to the era of insecurity.
As the violator of the rules, Prussia naturally drew considerable enmity. The most direct consequence was that during the Prussia-Denmark War, various nations lined up on the side of the Danish people.
Of course, this does not prevent everyone from supporting the Prussians in their confrontation with Russia. International politics have always been about supporting what is beneficial to oneself and opposing what affects one's interests.
In St. Petersburg, the whole world was waiting for the Tsarist Government's move.
If it were the era of Nicholas I, the response would have been a simple one—fight. With its strong power, crippling Prussia would not be difficult for the Russian Empire.