Ice floats. This shows that ice is less dense that water. When ice melts, it occupies less volume.

When ice floats, most of it is submerged and a little sticks up above the water. The change in volume leave just enough water to fill the submerged part of the ice. This means the water level does not change when floating ice melts.

A lot of the ice in the arctic is floating on the Arctic Ocean. No rise in sea level will come from that.

Antarctica and Greenland are another story. The ice is on land. When it melts, it flows into the ocean and raises sea level.

And as you say, raising the temperature of the top few thousand feet of the ocean will raise sea level from thermal expansion.

Ice floats in fresh water. This shows that ice is less dense that water. When ice melts, it occupies less volume.

When ice floats, most of it is submerged and a little sticks up above the water. The change in volume leave just enough water to fill the submerged part of the ice.

Sea water is a little denser than fresh water. This means a little more ice sticks up above sea water. When floating sea ice melts, there is a little more than enough to fill the submerged part.

A lot of the ice in the arctic is floating on the Arctic Ocean. The rise in sea level from that would be small.

Antarctica and Greenland are another story. The ice is on land. When it melts, it flows into the ocean and raises sea level.

And as you say, raising the temperature of the top few thousand feet of the ocean will raise sea level from thermal expansion.