As was the case with its war on Finland: to keep hammering away, relentlessly with its larger size and numbers, heedless of costs, until the other side buckles under. At bare minimum the conditions for that mean: to make the annexations that are now ingrained into its constitution - and have largely become facts on the ground, with a nearly unmovable front line - facts to be officially recognized by the other side and by international law.
It has put itself into a position that if it were to withdraw in violation of its own constitution then that would also destroy the legitimacy of the Russian Federation, itself. So, the only way for it to lose, now, is revolution and/or overthrow of the government. It's left itself with no other way out. The talking point that it has been issuing, almost from day one, that this was an existential war, is no longer propaganda, but a fact - a fact of its own making.
For that reason, it must now adopt the dictum: pursue it until you die. Whatever the cost.
An example of what might be considered a way out of its quagmire would be the recognition of the current de facto boundary, that the stalemate has settled upon, nearly unmoved for the better part of a year now, but at the cost of relenting on Ukraine becoming part of NATO and the European Union. It gets land, but loses the cause that led it to its action in the first place: that of reincorporating Ukraine, in its entirety, and possibly other parts of the former Soviet bloc, back into the fold.
The immediate predecessor of its 2022 action was, actually, not so much what led to its earlier 2014 action, but Ukraine's de facto 2018 withdrawal from the CIS. It was never fully a member, in the first place, but this hammered the final nail in the coffin of the whole enterprise. The CIS was the last remnant of the former USSR. This is also why Russia took the actions it did against the other marginal member states: Moldova and Georgia. Moldova is actually still in the CIS, by the way, except Moldova has backed further out of it in 2022. Georgia backed out of it in 2008.
With this slow-walk collapse, all hopes of restoring any semblance of the former order (except by force) have come unraveled.
Putin has, pretty much, styled himself as the Aurelian "restorer of the world" of the Third Rome, if not in word then by policy and deed, when the reality of the matter is that he is more akin to being the Justinian of the Third Rome, the "king" of "all the king's men" who could not put humpty dumpty back together, and the self-styled "restorer of the old order" whose legacy upon his death was (and shall again be) the almost immediate unraveling of everything he sought to accomplish, and the undermining of his whole life's mission, and reduction of all that once was into becoming nothing more than the glorified Rump State, that Russia - with a population barely as large as that of Japan, Mexico or the Philippines - already is.
Like the empire under Justinian, Russia and its ambitions on restoring the old order, will continue on as long as Putin remains alive - but only as long as this. Power has become so concentrated at the top, that a fatally critical dependency on that concentrated leadership has developed to such a degree, that when the top is lopped off by the inevitability of senescence, already clearly visible to see, there will be nothing but a vacuum left behind ... a dangerous vacuum that (like the Russian FM, himself, noted in one of the few assessments he got right) could lead to rise of several nuclear-armed Asian warlords in place of just one.
It bears in mind, that Russia's real existential threat comes from the East, not the West. The national PTSD trauma frequently cited of it is not with respect to its history in the 1940's, 1910's or 1810's, but (as I pointed out to the author of the above cite, who is now an acquaintance) is with respect to the far older history of its 300-year Beat Down and occupation from the East - a history that it is now slow-walking itself back into. The fear of that trauma (which I've seen surface a few times on Russian talk TV, e.g. "Russia’s defeat would resemble the Mongol yoke, with a modern technological twist") is its Achilles heel. It will be receptive to concessions, like the NATO + EU one pointed out above, because it needs to be rescued from its, now de facto, subjugation and vassalage to the East. But other than that, or the death of Putin (if even: noting the above remarks about a multiplicity of Asian nuclear-armed warlords), it will pursue its military action until it dies, for the reasons cited.
