The Mayor of Kiev already announced that the "surrounded" quote was bogus and not true. I would take this story, just like the "surrounded" story with a huge grain of salt. Both sides are furiously spinning tales of victory and defeat.
Russia can obviously prevail in this war if they press their military advantages. The question is how far Putin will go and what political price is he willing to pay.
And how far his Generals will let him go.
It seems to me that if the Russians want Kiev, they will have to kill tens of thousands of civilians. Would NATO permit this. Using air power, Russian formations can be readily destroyed. Hard to believe Putin would use nukes to retaliate.