Pretty sure you have it backwards. It is a measure of the upward force, or buoyancy, and is calculated by the weight of the object in general - the weight of the object in the liquid in question. Volume and density of the object are not directly addressed in Archimedes' equation.
The amount of possible rise has been definitively calculated. It is 215 feet or so above current. So there will be no Waterworld. That is actual scare-mongering.
Obviously we don't have to get close to that for there to be some serious issues with all the populations that will be displaced at even 50 feet above normal.
Antarctic sea ice is also not a relevant factor. What if sea ice is growing because of melting land ice?
The most recent measures show that the loss of land ice has
dramatically accelerated in Antarctica. I'm sure there are brief periods where the continent catches enough snowfall to overwhelm the trend, but the trend is clear.
Antarctic Land Ice Loss by Decade
was 40 gigatons per year in the 70s and 80s,
was 50 gigatons per year in the 90s
was 166 gigatons per year in the aughts
was 250+ gigatons per year 2009-2017