The comments about peace negotiations by Lavrov are interesting. Putting on my "eternal optimist" hat, I'm wondering if renewed negotiations between Kyiv and Moscow might give Russia a way out of this debacle. If Russia can secure political assurances from Kyiv to improve the way in which Russian-leaning people in eastern Ukraine are being treated, then Moscow can claim to have achieved its goals. There might just be the vaguest glimmer of hope for a political situation right now.
Think about it...the Azov Battalion was destroyed at Mariupol so Moscow can claim to have "de-nazified" Ukraine's military. Assurances about better treatment of pro-Russian people in the east will address causal factors for the fighting there. Such agreements could enable a ceasefire to be brokered and for Russian forces to withdraw.
Now....removing the "eternal optimist" hat, I'm not naiive enough to think this will happen quickly. Such agreements would still leave Russia in control of Crimea which Ukraine won't want. Also, any negotiated withdrawal by Russia, despite whatever positive spin Moscow puts on it, will be seen as a humiliating defeat, with the big, bad bear backing down in the face of a much smaller adversary.
However, Ukrainian offensive successes have changed the context of the war and Moscow is under increasing pressure to either win decisively or find a way out. They can't order a general mobilization because they simply lack the resources to train and equip such a large force....plus it would take months before any decent forces could be sent into Ukraine. Other than nukes, there aren't many other good options on the table to bring about a Russian victory...and if you can't win, the best you can hope for is some sort of negotiated settlement that at least allows you to save face. At worst, it will be an all-out defeat which could cause Russia itself to implode, much as it did after the break-up of the Soviet Union.