This is the thing, everyone is dealing with this crisis by asking "What will Putin do?" without considering that the rest of the Russian public are not clones of Putin. If the Russian economy collapses, and it will, then sooner or later the people at the bottom AND the top will want it fixed, and if the West stands firm on keeping its sanctions up they will realise that the only way to do so is to stop the war.
This is also true of Russian military officers though. Leaving aside the economic situation which has far less precedent, Putin may be livid that Ukraine didn't just roll over but that doesn't mean that his military thought it was the only possible outcome.
They started in a way that showed they were trying to minimize causalities, and that includes the infrastructure of Ukraine for the previously made 'rape, loot,
then burn' point. But that's not worked and the captured plans from the Russians shows their time table was taking Kyiv in something like a fortnight. This means they're not even that far behind their plans. More than this, it appears they tried to take some cities (robbed some banks and electronics stores while they were there, who wants to take two trips downtown in a week?), it didn't work, but far from being
driven out they
pulled out.
Then they encircled the cities. The step up in rocket and conventional artillery echos, heck is a direct copy of, old Soviet encirclement of population centers. This will escalate to more bombings if their air power holds.
The logistics might well be a true **** show, but maybe less of one than it initially seems because they are operating just beyond their normal max ranges. They've taken more airports now and their big convoy lines seem to be working as one would expect. If they switch to not operating outside their normal max, we could see the food/fuel issues seriously reduce. I hope this isn't the case and their logistics actually worsen due to the sanctions and other problems (inefficient corruption seeming being the primary factor).
Putin might be behaving irrationally but that doesn't mean the actions on the ground are irrational in the same way, if at all. Sending in poorly equipped and trained troops isn't outside the realm of rational possibly tactics, even if one can argue it isn't optimal. The Russian military just doesn't care about those casualties in the same way we would.