I could imagine the Russians moving in to the Donetsk and Luhansk oblasts, where Russian-speakers form the majority, and Putin could claim to be liberating the Russian-speakers from violence and oppression from the Ukranian majority. But a land bridge would require conquest of Kherson and Zaporizhia, which seems highly unlikely. It would be infinitely simpler to construct a bridge across the Strait of Kerch, which is barely two miles wide across placid waters. If they conquer all the way to a land bridge at Armyans’k, it has little to do with establishing a land bridge and everything to do with conquering the entirely of Eastern and Southern Ukraine... which I don’t see as likely.
Ukraine could lose everything south of the Dnieper, from Donetsk to Meltipol, to Crimea, IMO. I don’t think they will go after the two cities, though.
Why would Putin want those problems?