Also, would Poles really object to a personal union with Russia all that much? One positive of this would be additional Polish Lebensraum further to the east, in Russia proper.
Yes, for many reasons but mostly for principle. The second thing is rather a result of the Russian overseer which is impossible to combine with the Polish style of government and as a result you would have a large group of people in Russia who would strive to pacify Poland as much as possible because Polishness in such a system will very quickly regain its position before Peter I. (See that the Prussian and at the same time German style of government did not work out, which strongly weakened the already weak position of the Germans during Elizabeth. (Look at the fact that the Prussian and at the same time German style of government did not work out which will strongly weaken the already weak position of the Germans during Elizabeth).
The Commonwealth will benefit from it more than Russia despite the fact that Russia is theoretically the dominant party. It will get a huge Russian army to support it and the outbreak of revolution in France may finally convince it to allow Poland to modernize its army. The outbreak of the Revolution in France may finally convince Poland to allow the modernization of its army, as well as the improvement of the central government, because in Warsaw of that period, as a result of the Revolution in France, it was boiling over. And it was close that the revolution could also break out in Poland.
But here I have to point out another small fact. Namely, the defeat of Prussia and their enlightenment power can strongly undermine the existing class relations with the disappearance of Junkers. It may, but does not have to make that in Berlin also will break out a revolution and the Republic of Prussia will join the French Republic as an ally.
And one more fact why it was almost impossible to keep the Commowealth in a personal union.. Namely, the lack of a pro-Russian party. You see, there was nobody pro-Russian in the Rzeczpospolita, everybody was ready to call on the Russians if anything happened, but nobody was going to be pro-Russian.
Even the famous Targowica, which is a symbol of disgrace and national treason, (not rightly to the end, the real traitors were those from the confederation of Grodno, many of the Targowicz were sincere patriots and thought that in this way they save the Republic from the wrath of Russia, but as it later turned out they came out on it badly. But Targowica was accepted because it sounds good as a symbol of betrayal, why? Because Targowica in English will be called Market City, Markettown. It fits better with the symbol of treason right?)
Of course I don't believe that there will be a Persolnal Union between Poland and Russia because we have to deal with a woman on the throne and there is no tradition of women rulers in Poland. Peter III may be considered by both sides as impossible to put on the throne because of his love for Prussia. Catherine II is the same as Elizabeth.
Another thing is also the aversion of Poles to a dissenter on the throne. You see well, the aversion to a dissenter in a tolerant Poland. How so? Simple, prostestants and orthodox Christians with time were considered dangerous for the existence of the Republic because by their faith they felt more connected with their fellow believers from other countries than with their compatriots.
The Deluge did not help in this especially when many Protestants surrendered and went into service to the Swedes. But the final blow to religious tolerance in Poland was the Tumult of Toruń of 1724, in which the Protestant and German population of the city broke into the Jesuit college, destroying and burning it.
This finally turned the tide of bitterness for many, and the guilty 20 were dealt with severely. And at the same time for the nobility who in OTL was ready to give the throne to anyone but under one condition, he must be a Catholic. And the Russians would not put up with a Catholic tsar. So they would have chosen someone else to be King instead of Catherine II's lover. Literally it was the worst choice of all because it pissed off everyone in Poland, but well Kaśka wanted to show that she could, so she did, it's just a pity that in general Russia had to put up with us because of it and her previous allies became a threat to Russia over time.
As for Lebensraum, sorry but it won't happen, if it does Russians will tear off some piece, maybe the one from the first partition from the Commonwealth. They were already talking about moving the borders to the west before the partitions.
Although there is a certain possibility that Peter's son, Pavel may be accepted by Poles but not necessarily by Russians. In the end, it may come to a peculiar curiosity if the Personal Union took place and Russians after some time want to get rid of him. Pawel would escape from Russia to Poland with the help of the rebuilt army of the Rzeczpospolita to try to regain the Russian throne. Which was more possible than in the case of Napoleon, because in order to conquer Russia you had to have the territory of Belarus under your control before the war. This makes it easier to march on the center of the Russian state.
OTL Paweł is quite well remembered in Poland, and he has a rare trait among Russian Tzars in the form of favoritism toward Poles. What de facto makes Pawel the only good tsar in Polish history. The only other one is only half of Alexander I, his own son.
It is quite funny that his second son Konstanty was a true Polonophile and polonized significantly.