My best guess is very similar to you fourth scenario.
I think, that one of the main Putin's goal (maybe his very terminal goal, but I'm not sure) is to solve the Ukrainian problem, and then quit the game as a triumphant (after president's election at 2024; but he has option to continue work on it until 2030, if he choose so and nothing changes significantly). Putin's time is relatively short - he is 69 years old, and there are some rumors (not very reliable, thought) that he is somehow sick. So achieving his main goal in two years is very preferably to him, but there are still another six president's years, if he need it and can afford it.
Ukraine is one of few ex-USSR republics that is not loyal to Putin's government, and he obviously perceive that as a big problem. So the main Putin's current goal, as far as I can assume, is to create artificial loyal states (on the basis of pretending to independence Donetsk Oblast and Luhansk Oblast of Ukraine) between Russia and NATO. There are already couple of such states with limited recognition around Russia (Abkhazia and South Ossetia, both of which are commonly recognized as parts of Georgia), so it is appropriate way for Putin to create a buffer zone.
Installing a puppet government at the Ukraine, as far as I can see, is the secondary goal, but also desired.
Speaking of price of the invasion in terms of Russian economics, there is Russian National Wealth Fund, which continuously grew up during almost all COVID pandemic. There were thoughts earlier, that this NWF was intended for possible war (especially considering, that pandemic was not reason to spend it). Today I say news, that government is planning to spend it to support the economics (personally, I consider it as a relatively good sign - if they started to spend the stock for a rainy day then they currently do not plan to escalate current situation even further).
I think that "blatant lies" case applied for newcomer real estate developers (RED); but well known RED can use their reputation and common knowledge about this reputation as part of simulacrum-3.
If there is common knowledge about many previous successes of this particular RED, then the bank can believe that everyone else will hunt this stag. Thus, the bank will sign the papers.
But newcomer RED can't afford just to pretend to pretend that everyone else is hunting the stag. The bank will not believe that RED's intention to build the skyscraper will be sufficient to convince other parties to hunt the stag. The RED must pretend that other parties already signed the papers to convince the bank to hunt the stag.
So, without good reputation, you must use blatant lies (S2) to convince people to hunt the stag. But having such reputation (and common knowledge about it) you can just pretend to pretend that you stag is the best choice (S3) - people will gladly join your hunting.