I learned that ice has a (slightly) lower density than water, hence it usually floats. I was convinced that submerged ice is doing so because of an additional weight on top of it (above-water ice pack).
Maybe there is also ice that is submerged without this extra weight, but then its density should be lower than water.
Either way, I don't see how submerged ice could take up exactly the same space when melted. If it has a different density, it should change in volume (elementary physics).
When that ice melts, it still weighs the same amount and fills exactly the amount of space that it was displacing. In other words, it fits perfectly in the space in the water that it was already occupying.
So floating ice that melts (above or below the water) doesn't change sea levels at all.
Only melting ice that is currently supported by land will increase sea level.
Liquid water is notorious for having almost no thermal expansion, but the little bit it does have will be multiplied by the volume of the ocean, then divided by the surface area of the ocean, yielding the rough vertical rise.