I thought he was just that, a great reformer, unlike his wife, who oppressed them.
Bingo
In my studies he came across as a truly bizarre character who cared nothing for Russia and switched sides during the 7 years war for little reason other than his taste in uniforms.
Peter didn't switch sides exactly. he made peace and ended Russia's direct participation in the war. The reason he exited the war is because he recognized no matter what Britain had won the war. He also thought that Prussia had been sufficiently ravaged as humiliated that a dismantlement was unecessary. Essentially, Peter understood the strategic situation had changed a lot from the beginning of the war and it was no longer best for Russia to continue fighting on the French side.
In my view, he could very well have been known to history as an eccentric man who nevertheless helped Russia if things had been different. The same goes for Paul.
Eccentric?
In this timeline Prussia and Russia would be allied and it's quite possible perhaps even likely that Fritz could convince the Peter to go along with atleast 1 partition That would allow Russia to add strategy depth and allow Prussia to Connect east Prussia with Brandenburg
Russia and Prussia were also allied OTL, from Peter III to the French Revolutionary Wars. Russia has a massive buffer, it doesn't need to sacrifice it for strengthening Prussia.
Perhaps not and the war certainly wasn't popular in the leading circles in Russia, but his animosity towards Denmark had a dynastic reason. Peter was son of Duke Karl Frederik of Holsten-Gottorp (his lineage to the Russian throne was through his mother) but his father had been severely mauled by Denmark in the Great Nordic War in the early 1700s - Peter sought revenge for that and wanted to reinstate his dynasty's rule over large parts of Slesvig-Holstein.
Considering the Russian wish to get access to the seas it wouldn't necessarily have been a bad idea to destabilise Denmark and eventually control it and the Gottorp dynasty anyway had a very old rivalry with the Danish Kings (of the Oldenborg dynasty). I agree however that by 1763 Prussia probably ought to have been the main object - it was big and closer and almost done, and East Prussia would have been a nice bite.
An additional reason Peter wanted to take Schleswig is to increase Russia's influence in Germany.
Prussia would not object to Russia's war wth Denmark-Norway. As part of Prussia and Russia's alliance Prussia promised to diplomatically support Russia in the crisis. Prussia kept this promised because Russia scared him completely and entirely, especially when Prussia was still devastated from the Seven Years' War.
Why would East Prussia be. Good bite? It is far away and filled with Germans and Poles. Historically Elizabeth didn't even want to keep it.
The problem was that controlling Denmark would have weaken Russia as it would have served to create hostility from France, Netherlands, Sweden and UK. Also it was doubtful Russia could defeat Denmark, Denmark had a naval benefit, and any war with Denmatk had to be fought far from home. Even if the Russian army won, the Danes would just retreat to the islands and unless we saw a Ice Winter, the Danes could simply just wait.
Alliances and marriages between the two dynasties would make a lot more sense, and selling Gottorp for Oldenburg or just money.
Controlling Denmark? The intention was not to control Denmark. The intention was to take Schleswig and reunite it with Holstein.
France and Russia were already on bad terms so to Russia making a separate peace.
Netherlands would have been concerned as they always had a keen interest in Baltic trade. However, the Netherlands were on little position to effect the Crisis or the followings War.
Sweden was ruled by Peter's very loyal uncle, who would never have betrayed Peter. And if I recall correctly Peter may have invited Sweden to partipate in the conflict against their eternal rival of Denmark, but Sweden declined due to their financial situation being poor against their failed participation in the Seven Years' War.
At the time Russia actually had a strong navy, not as strong as Denmark's but not anything that could easily be ignored.
The war with be far from Russia but close to the Russian held Holstein and Kolberg, which was intended to act as a supply depot once the war started.
If the Danes retreat to Fyn then the Russians can occupy far more than just Schleswig (which is all they desire), so Russia wins the war.
The question comes up with what of Ekaterina? Does Pyotr being better adjusted mean the marriage goes better? Or does Katya still forment rebellion against her husband? And if so, how does Pyotr react to this?
Catherine is still likely to not be loyal to Peter considering her character. However, if TTL Peter is not a reformer he is unlikely to upset the two guard regiments he did OTL, the two guard regiments that launched the coup.
Basically agree and the Danish Army marching in Mecklenburg on the Russians in 1763 wouldn't have been a walk-over either if they had met in combat. Denmark-Norway in second half of 18th century had earned huge sums on transporting goods for various war waging nations and some of was used on army and navy and a very competent French General (Claude-Louis de Saint Germain) had been hired to organise, train and lead it. British observers described it as a very very impressive force, not at least the cavalry.
But still, we don't always chose what from the future would look the smartest and Peter certainly had a "family issue" with Denmark.
His wife Catarina didn't and in 1773 formally agreed to the Danish annexation of the Gottorp parts in S-H.
The war certainly would t have been a walkover as you correctly state the Danish army was competent. However, it was against a larger, more experienced, more competent army led by one of the greatest Russian generals of the time, Rumyanstev. I mean you have to remember the Russian armies were the ones mainly responsible for devastating Prussia during the Seven Years' War.
