Congress of Kopenhagen:
The first world congress was held in Kopenhagen. This congress would be catastrophic for Russia, ottomans would request Constantinopel, and Catherine would never accept such claim.
Catherine requested Finland. Russians settled Karelia many years before Sweden.
As russian diplomats already knew, the congress wanted to give Konstantinopel to Ottomans. A global war was inevitable.
Modern historians say that this is the first global scale war. However, it includes many different war theatres, and regional wars remained in history separately.
In western Europe and middle east the war is known as "war on russian imperialism", while in China it is known as "sino-russian war". Although, the war was declared to halt Russia's expansion, Catherine sought it as the opportunity to solve the border disputes of the empire.
Prussia has signed diffencive pact with Russia some years earlier. So, when the war spawned Prussia allied with Russia. However, some days after that King of Prussia declared war on Russia. Prussia was at a worse foreign situation than Russia. It was at war with almost anyone. The prussian mystery is a well known event, that even modern historians can't understand.
The strange Prussian behaviour was the best Prussians could do for Catherine. Prussians would keep occupied the French and the Polish, while Russia could act without caring a lot about central Europe. Although, Prussians were at war with Russia, they wouldn't try to attack, France and Poland were worse threats for them.
War preparations:
With Prussian agreement cancelled Catherine resigned the traditional defencive pact with Portugal. Good thing, Portugal remained out of the war.
However, Iran was in the russian side and completely helpless. Mughals and Ottomans were at war with both of us. Catherine gifted them the appropriate knowledge to stand alive.
Italian front:
Russian controlled a military base in Naples, Italy. French army was in medieval ages, so capturing papal states was easy.
Catherine decided to sign a peace treaty with France. Although she gave back Naples, she controlled Rome, and being at war with anyone wasn't a good idea.
Italy after the treaty of Veneza. Russia keeps the papal states, France regains control of naples and Portugal keeps control of Veneza.
Anatolian fronts:
At last Russians captured Derbent. Moreover, for an unknown reason, the roots from anatolia to Derbent were destroyed. So caucasian front was secure from immediate attacks.
Muslims "supported their ottoman brothers to liberate Konstantinopel."
Chinese fronts:
Chinese were even worse than the French, although they controlled a considerable army in Korea. They lost Kashgar. The chinese empire was extremely unstable.
In a surprising movement Chinese conquered Ulan-Udeh. Russians corrected their mistake soon.
Russians captured chinese capital in an attempt to capture the Ming ruler and put an end to his reign. Unfortunately, he fled and although the Chinese empire was collapsing it stood the hit.
Russians captured the chinese military base of Kanggye in Korea. Although not an important city it had the effect Catherine wanted. Chinese warlords declared their indepedence from the Ming and broke in small warring states.
Finnish front:
Maybe it is time to "discuss" with Sweden and England who controls Finland and Alaska.
Other results of the war:
Argentina collapsed like China.
However, Russia experienced extended foreign isolation. Although it won the battles, the economy was ruined. Russian economy lied on exports, and exports gone. Fortunately, taxes could only pay maintainance, but for how long? If this continued rivals would de facto win.