The presence of sea ice changes the level of the sea not one whit. Ice is lighter than water, which is why it floats on top, and does not displace more water when it melts.
Try this with several ice cubes in a glass of water, then fill the level of the water to the point where a meniscus held in place by water tension rises slightly above the rim of the glass.
Let ice melt.
Observe spillage on the surface on which the glass stands.
The meniscus above the rim of the glass shall be exactly the same, there will be no spillage.
When they talk about ice melting to raise the level of the sea, they aren’t talking about sea ice, they are talking about the melting of land ice on Antarctica and Greenland.