This is one of Vox's Future Perfect predictions for 2023; they give it an 80% probability.

This past year has likely been the worst for Putin’s survival chances since he first ascended to the presidency at the end of 1999. He launched a brutal and illegal war that made his nation an international pariah; the resulting sanctions and mass mobilization of young men from that war are wreaking havoc on an economy that’s also suffering from now-falling oil prices. On top of all that, he’s losing that war to a country with less than a third of Russia’s population. All of these are conditions where coups start to become imaginable.

That said, it’s important to keep “base rates” in mind: How common are coups in dictatorships, generally? A 2021 paper from John Chin, David Carter, and Joseph Wright looked through a database of coup attempts and found that in autocratic countries, 6.3 percent of years featured a coup attempt. “Regime change coups,” their term for attempted coups that totally change a country’s governance structure (as opposed to, say, replacing one general with another), are much more common in personalist regimes like Putin’s, with attempts in 7 percent of years. But in general, only 48 percent of coup attempts they studied succeeded.

This paper might lead one to think there’s perhaps a 3.5 percent chance of a successful regime-change coup against Putin in a given year (and it’s hard to imagine a coup against him that doesn’t constitute a regime change). Given all the stressors listed above, I think that’s much too low an estimate. That said, the low overall rate of coups makes me think it’s more likely than not that Putin stays in power.

(Vox)

Resolves according to Vox Future Perfect's judgment at the end of the year.