@alexmilman would and he'd probably explain it better than I'll be able to do.
Thanks. This, actually, was explained multiple times in various TLs so I’ll be repeating the things which are already generally known.
1. As far as the Russian interests were involved, there were none except for a rather vague idea expressed in a memo of Elizabeth’s conference. This specific issue had been discussed to death on this forum and the relevant parts of the original document quoted and discussed pretty much sentence by sentence so I’m not going to quote them in the (n + 1)s time. Enough to say that the idea boiled down to two main items: conquer East Prussia and exchange it with the PLC for Courland and hopefully also get from the PLC some unidentified territory on the South that would open access to the Black Sea (to which the PLC did not have an access). Neither idea was discussed with the PLC and none was realistic in political terms. Which left the only item: weaken Prussia to prevent its influence in the PLC. None of these goals was of a slightest interest to the Russian nobility so the war was not popular to the get go. The war was strictly a cabinet war with no national interests driven exclusively by Elizabeth’s feelings and Bestuzev’s adherence to the “Austrian alliance no matter what”. That system already demonstrated its “worthiness” when Russia was forced to give back pretty much all its gains in the Ottoman war of 1735-39 but the Chancellor stuck to it (and to Austrian bribes).
2. It proved to be very costly and the Austrian subsidies were not covering the expenses (not sure if Elizabeth was spending all received money on war but this is irrelevant) and by the end of her reign the troops were not paid for more than a year.
3. The losses were huge both from the fighting and from starvation and diseases. To compensate, the new recruits were needed and they were coming from the nobility’s estates.
4. In theory, when the Russian troops reached Prussia, the supplies were expected to come from the Austrians but they could not/would not provide enough from already exhausted Bohemia so the Russian army had to organize its own supply system which started working marginally satisfactory only after more than a year being based upon appropriating food from Poland and East Prussia. Both were exhausted more than a year prior to Elizabeth’s death. As a result, there was a need to launch a special rather complex operation for taking Kolberg to allow bringing supplies from the RE by the sea.
5. After Kunersdorf general position of the Russian command was that the Russian army accomplished enough and now it is the Austrian turn to act aggressively, which was (among other factors) not Daun’s style of a warfare. Difference of the opinions resulted in alienation that culminated with Buturlin’s appointment: he simply held his troops in PLC guarding the supply warehouses and preserving soldiers’ lives while ignoring Elizabeth’s orders. The token events like raid on Berlin were changing nothing strategically.
6. From the Russian perspective the war did not have too much sense at the start and after Elizabeth’s death it lost whatever was there: why should Russia keep fighting for the Austrian interests? Even more so, why to fight for the French interests if Louis XV was quite open in his policy to keep Russia weak and to minimize its influence in the PLC? Majority of the nobility was seemingly happy with peace and after Peter’s Manifest of the Nobility’s Liberty got plain excited.
7. Who were most vocally upset with the peace making noises about the lost glory? The Guards who did not participate in the war and remained at St.Petersburg. Who, among the participants, was making the loudest noises? Bolotov, who spent most of it in East Prussia and in his memoirs collected all nasty rumors about its conduct and behavior of its participants. A classic “eyewitness who was not there”. Who was the most enthusiastic supporter of PIII in the army? Its best general Rumyantsev who, probably due to an absence of Bolotov’s patriotism and strategic genius of Grigory Orlov, was quite happy when it ended. Chernishov, presumably general #2, was gladly commanding Russian corps sent to help Frederick, received Order of the Black Eagle and agreed to Frederick’s request to delay, after the coup, departure of his troops allowing Frederick to win an important victory by their presence. Interestingly enough, out of all leading generals Rumyantsev did not get any award from Catherine for his performance in the 7YW.
8. Catherine. As a Grand Duchess was pro-Prussian, which made Elizabeth extremely angry. During the reign of PIII became a member of the “patriotic” party of the Guards (see above about their contribution) and a part of the court clique which by various personal reasons did not like Peter. After the coup not just left peace agreement in force but accelerated removal of the Russian troops from Prussia.
9. Now, as far as the initially expected award, Courland, was involved, Russia was controlling situation there and a duke was sitting on a throne only as long as he was permitted. Elizabeth kept the legitimate duke exiled in Yaroslavl allowing King August III to appoint his son as a duke bypassing the PLC law and wishes of the local nobility. When Catherine “forgave” the old duke the appointed one was kicked out without much ado: it took a single battalion of the Russian troops to be
present and the Saxon duke, after being advised to vacate residence voluntarily, promptly left and the old duke returned. All protests from Warsaw were ignored. So did it worth to get into a major war for
that?