I might very well be mistaken, but this war and Russia's belligerence during the last 10 years never seemed to me a matter of ambition and territorial expansion, but rather desperation. Putin is 70, and his death will certainly plunge Russia into a period of turmoil. It doesn't matter if a successor is anointed by big P himself. The democratic opposition will see it as an opportunity for reform. The political and military elites will be fighting each other to advance their position. I'd be surprised if after Putin's death the Russian state could settle for a coherent agenda and foreign strategy within a decade.
The last time Russians found themselves in a similar position, NATO and the EU showed up at their doorstep. Baltic countries, Poland, Czech Republic, Hungary, Romania, Bulgaria... all of them joined NATO and/or EU in quick succession.
That's what I think Putin is trying to prevent. So the goal is to either have loyal buffer states (e.g. Belarus, Kazakhstan) or leave "unruly" buffer states (Georgia, Ukraine) in such state of destruction and disarray, that after Putin's death, Russia could get back on its feet before those states could focus again on entering international alliances. In other worlds, if I need 10 years to recover, I'll make sure you need 20 years, even if it adds a couple of years to my tally.
Of course this need of keeping NATO at bay exists only if the economic and political strategy of the state is to be an international gun for hire. It's a pity that the Russian elites decided to go for the easy buck with gas and military instead of developing the huge technical and artistic talent of the Russian people.
The irony is, after Iraq's invasion, NATO was incredibly unpopular in many European countries, and actions against Russia were seen as undesirable. I think fellow Europeans will agree that we saw Russia as an authoritarian state with old-fashioned values, but we were hopeful that one day we could have shared institutions and deeper political and economic cooperation. Now a lot of my fellow citizens perceive Russia as a direct enemy.