Cables are generally buried. So if this is true the cables would be underneath the new sea floor and not in immediate danger.
Cables in urban areas are typically in conduits under the street. If the streets are flooded with sea water they will have worse problems than deteriorating internet service. Parts of the cities would have to be vacated or relocated.
All of this would likely take place over centuries with plenty of time for normal technology changes to occur.
On the other hand, after Sandy, much of Manhattan’s communications infrastructure was submerged under water much higher than speculated here. A lot of copper cable was compromised, and then replaced by fiber suitable to be submerged.