I agree it’s strange, but I don’t think reintegration is in the cards, for numerous reasons. Whatever he goes for, there’s nothing Putin can or will do to uninvade Ukraine, or make us forget about Russian behavior over the last 20 years.
It’s clear now that Russia is a 19th century power that is purely about strategic opportunism to expand their borders, and who feel that blood and iron are the only true measures of a country. They have to be treated as such.
I think the fact that they aren’t backpedaling yet is an indication that they genuinely don’t believe they’ve lost at this point.
People paint the Russians as cartoon characters, for good reason - Prigozhin genuinely looks like someone who would spend entirely too much time trying to kill a pesky wabbet - but in the real world they’re not actually trying to lose, and they will do whatever they can to win.
So that probably means more mobilization and a push. After that we’ll know more about their options, although I suspect they’ll keep trying for as long as they’re able.
Some people are calling this a global ordering war. Once it ends, we will have to find an entirely new order under which to live with the Russians, which is also why it would be incredibly stupid of us not to pressure them as much as we dare right now, without risking adverse outcomes.
We need to act like there’s nothing of theirs that we want, including normal relations, and we need the Ukrainians to humiliate them as much as possible on the battlefield, because all of that adds up to leverage we will use in negotiations after the war.
I suspect that we will want to prevent Russia from collapsing completely (because civil war + nukes is a wild party) and I suspect that we’ll opt for some solution that maintains a strictly transactional relationship, possibly for something like gas or whatever we need. Sort of a Saddam-Iraq model.
How much we choose to humiliate them after the war is highly disputed. The right wing (by which I mean classic Republicans, not the Putin-romancers) want to turn them into Weimar Germany - which ironically speaks to Putins point about this having been the goal of the US all along - while the centre and left tend to have more concern for how that might play out long term, and are considerably more deterred by the prospect of a Russian break-up.
But I don’t think anyone beyond the worst loonies on the left and right are angling for anything that resembles normalization.
/edit/ I should’ve added that the left is also concerned with strengthening American hegemony