I guess you mean the shape of the countries doesn't change much? iirc the majority of Earth's population lives on coastlines, most major cities will be inundated
The rise in sea level is something of a misnomer, because the real damage comes in storm surges. Even a 1cm rise increases the amount of water that can pushed inland by *checks notes* a whole helluva lot. So while manhattan isn't going to be put underwater even after a whole foot of sea level rise (predicted by 2100), the storms it has to survive will be much worse.
People won't move just from a little water in the roads (just look at Miami), I think even in the year 2099 you'll have a hard time getting new yorkers to move to ohio, but once a storm comes through and destroys their housing they will have to find somewhere else to live.
But housing isn't expensive because it's hard to build. It's expensive because building it isn't allowed. If it all had to be rebuilt, that would be much cheaper than trying to build it under existing conditions.
Insurance isn't an endless bucket of money, and it's also going to adapt. Eventually you just won't be able to get insurance for properties in areas like that. Just look at the floods in New Orleans or the current flooding along the east coast of Australia, I doubt there's enough money to make all those affected whole again.
I think insurance may be the main driver for when people actually decide to move. People are pretty resilient, but if you can't get a home loan because you can't get insurance, people won't keep living there.