There is no evidence they are regrouping. There is strong evidence of vehicles being trained back out of Ukraine via Belorussian rail. To attack kyiv again would be starting from scratch.
Putin’s approval rating is irrelevant.
Russia has managed to lose the battle of kyiv, and among other blundering failures, has repeatedly failed to establish air superiority. The extent to which they would be utterly slaughtered given actual western air support is hard to exaggerate.
At least to the extent of arbitrary Europeans needing to worry about a draft.