The fact that it's tiny and with massively reduced revenue streams would result in its army being tiny. During the First Silesian War Prussia was scraping the barrel to field an army of around 30,000.
The number would be meaningful if not the couple things:
1st, Austrian army at that time was even smaller (at Moliwitz 21,600 Prussians vs. 19,000 Austrians) and had to be built up during the war (ditto for Prussia).
2nd, by the beginning of the 7YW size of the Prussian army was approximately 150,000 so what it had at the beginning of the 1st Silesian War is quite irrelevant.
After the 7YW it was maintaining an army of 160,000 (1768) - 190,000 (1786) which means that even with the loss of a half of its population it would be able to maintain a standing army of 80,000 - 90,000 with a possibility to increase it if needed. Taking into an account a general quality advantage of the Prussians circa 7YW, not too bad (for a while).
Hapsburg empire with a much greater population had at the start of the 7YW an army of approximately 200,000 and approximately the same number by 1778.
France (the biggest population in Europe): 1756 - 330,000, 1786 - 156,000
Russia: 1756 - 340,000 (but it would be able to send only a fraction of that number to any specific theater of war).
Now it has even less means to build an army and the period of massive armies is starting to dawn.
It will not kick in until the French Revolutionary Wars and Prussia was by far more effective in raising the armies, as a proportion to its population, then Russia, Austria or France. 160,000 out of the population of 2.5 millions means that even with the loss of a half population it would be able to have an army of 70 - 80,000.
Tilsit was nowhere near as Carthaginian as the peace the Austrian alliance had in mind.
What "Austrian alliance" had in mind was to get back at least part of Silesia and not let Fritz to keep Saxony. Elizabeth, as a part of this "alliance" just opportunistically grabbed what her troops conquered and, if anything, did not look for a complete annihilation of Prussia: Fritz was a bad guy but, if properly subdued, could be useful in a future against the Hapsburgs (relations had been steadily souring during the war almost all the way to a complete breakdown by the time of Elizabeth's death).
Um what?
See the numbers above.
Sadly I don't have access to my personal library at this time, I'd love to track down a citation for you.
As I said, did not see anything of the kind so please do. But, unless some serious contemporary documentation is cited, speculations are rather pointless.
Right Bank Ukraine is some of Europe's most fertile land and a large population which would yield a high amount of revenue.
In the late XVIII thanks to the better organization of farming a single serf on the very bad lands of the Baltic provinces of the Russian empire was producing to his master more income than 3 serfs on the most fertile lands in its "Russian" part.
The region was Greek Catholic and as previously seen in Left Bank Ukraine and as seen in Right Bank Ukraine when it was eventually annexed, that was very easily replaced by Russian Orthodox.
At the time of its annexation option of getting the Eastern Prussia was not on the table and general political situation was quite different so this is quite irrelevant.
The extended border with the Ottomans and their moribund vassal is a virtue rather than a vice, as Russia's general direction of expansion in that period was towards the southwest at the expense of the Ottomans.
At the time of Elizabeth wars with the Ottomans were not in the agenda and being subjected to the Crimean raids was not considered and advantage.