Stone Age settlement found under the sea in Denmark

Unfortunately I don't expect there is any particularly reusable solution to be uncovered. Ancient peoples facing rising tides almost certainly just walked a bit inland and built new huts there. They probably thought nothing of it. They were a far more physically mobile culture, without great dependence on immense, immovable infrastructure - nor on rigid land ownership rules.

Our culture's migration will be entirely different.

Been there, done that, it is worse than the alternative. People will stop cultivating anything, because why bother if a random officer can just take things from you at will.

Western regulations about land appropriation are strict for a reason, and they always require just compensation for a reason. That is the only way to prevent powerful people from just grabbing what they want, cloaking the thieving act in word bubbles about common prosperity.

Maybe there could be some balance instead of "Either everything can be owned, or nothing is!".

It isn't impossible to move cities if it's really needed and someone is footing the bill, even in a democratic Western country that is famously highly regulated, like Sweden. Since a mine in the north is expanding, they have to move the entire city (paid by the mine's operator in this case), building by building, which of course isn't without complaints, but it's a thing that actively being done as we speak. https://www.bbc.com/news/articles/cde3xp4xlw9o