Like the concrete Antonivsky Bridge in Kherson, the Chonhar Bridge might need a few more holes punched in it, to take it out. There is a land bridge to the West that is a few kilometers wide, that connects Crimea to the mainland, and another to the East, across the barrier islands. Pontoons and ferries can also keep some reduced supply flowing.
When Putin was talking his land bridge, he was talking safe corridor from Rostov on Don to Crimea. That is no longer the case.