You have all the powers that Putin currently does. Everyone completely loyal to Putin is now loyal to you. Enemies of Putin are enemies of you. Putin no longer exists, and there has been a clean and absolute transfer of power to you. The economic, military, social and political situations are the same as they now are. You are not inhabiting Putin’s body, you are just you. You’re magically transferred to the Kremlin. The world at large doesn’t know your past life, to them you have magically appeared as the new ruler. To everyone who knew you before, you just vanished.
Edit: no one knows your past life YET. They’ll quickly figure it out. You will not lose any support based on your actions in your past life.
Fortunately for OP, they didn’t use numbered bullets, so they’re safe!
Regular bullets work just as well, if you happen to fall on one during a quick exit from the upper floor.
If I were truly thrown into this scenario, my first step would be accepting likely death. Even if you maintain status quo and do no good, you’ll be killed by the next guy in line. There’s nearly no way to both satisfy the current oligarchs and maintain enough power to prevent being replaced by one of them. There is also no way out, as Russia has carried out assassinations in foreign countries. Not that you’d make it onto a plane.
So I really would try to do all that. I’d tell them that whatever force got me there also gave me time to enact failsafes so that, if I disappeared, every property that every Russian billionaire owned would make unexpected contact with drones. Then I’d go ahead and post Putin’s files with every billionaire’s dirt and holdings hoping to start some fires they’d need to put out before coming for me. From there, an aggressive push towards democracy by appealing to the people in the hopes that they’ll back me, which might buy a little extra time.
I think this secures a few hours. They won’t want to move against a complete unknown that suddenly became president. That’s enough to call Biden (allegedly to negotiate US withdrawal from Ukraine in exchange for election interference in Harris’s favor) and send him every bit of data on the military that I could. That might be enough deterrence to buy more time: “the US military knows everything now, so killing me might have consequences.” I’d CC several other NATO members, but for time’s sake Biden is probably the one to call.
Maybe I could get some bodyguards that appear loyal to me, maybe not. But every bit of bluster I could muster, I’d throw it down out the gate, then start trying to fix the country before they call the bluff.
Yeah, I still die quickly, but even a single step towards improvement is worth my life. An easy decision to make when it was forfeit the second I became president. Even if I failed miserably, merely dumping presidential documents would have been worth it. Perhaps it’d get the ball rolling.
Edit: I missed the part where everyone loyal to Putin would be loyal to me. That opens up a ton of space to actually set up these failsafes or move against the oligarchs myself, as well as secure the Kremlin with men more or less actually loyal to me (by wiring them all a million USD on the spot with promise of more). Putin put down a rebellion from one of the most powerful oligarchs, so there might actually be a way to survive long enough to do many of the things on that list. I’d probably not dump the oligarch files and keep that on a disappearance failsafe then proceed mostly the same hoping to generate serious, potentially irreversible momentum before dying.