If I may speculate here:
Is taking the country really the objective?
I think this is a remote objective. If this action nets you the whole country why wouldn't you take it. But I think all or part of the eastern provinces or at a minimum a land bridge to Crimea, is the main objective. Toward this goal you take as much of the country as you can and you give back some of it in peace talks.
Or to install a Russia-friendly government?
This would be a realistic goal if they capture Zelensky. Find a Ukrainian puppet. Let him or her negotiate the peace giving Russia the Eastern provinces. Then let the puppet deal with controlling the Ukrainian population.
Or is the goal to force Ukraine to become a non-aligned buffer state?
I don't think this is as suitable to Putin. But if Zelensky can sell it, it may save the Ukraine from further hurt. But I doubt Zelensky will go for it. Someone is feeding him bad intelligence that if he just holds out and lets his people suffer the Russians will cry uncle first due to the sanctions.
This, however, presupposes that Putin cares about Russian public opinion. I wouldn't put it past Putin to give his people a choice: Suffer, shut up and live in relative freedom OR be drafted with half going to Siberia and the other half to full time occupation of the Ukraine getting shot at occasionally by Ukrainian civilians.
Or to push Russia’s border further from Moscow?
As I have already stated this is the likely fall back goal. Take the eastern provinces in a peace deal. You have your land bridge to Crimea. You likely can continue to exert pressure on the rest of the Ukraine for many years to come.
Smartest thing I’ve seen here- or anywhere.