The sea level rise being talked about here comes from the Gulf Stream slowing down.
The Gulf Stream is the current along the east coast of North America at the surface (red). The Atlantic Meridional Overturning Circulation (AMOC) consists of the part of the Gulf Stream going north to Greenland, sinking, and returning south at depth (blue).
The Gulf Stream speed impacts sea level on the coast within months. This, like the existence of the Gulf Stream itself, is a direct result of the earth’s rotation and is very well established.
The Gulf Stream can’t just pile up water in the North Atlantic. If the AMOC sinking stops, either the Gulf Stream slows, or more water returns south at the surface, or some of both. Sea level rise depends on how that plays out.
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2019JC015152
“Observational analyses focusing on shorter (generally less than decadal) timescales show robust relationships between some components of the North Atlantic large-scale circulation and coastal sea level variability, but the causal relationships between different observational metrics, AMOC, and sea level are often unclear.”