A simplified explanation of La Nina is, equatorial winds blow from East to West in the Pacific Ocean. These winds cause upwelling of cool bottom water which is transported West to the Indian Pacific Warm Pool. It warms along the way. The collapse of the East to West winds causes this stacked up water of the pool to slosh back to the East and we then have an El Nino. Papers have discussed La Ninas and changes in sea level rise.
Say warmed water sinks. Still contributing to sea level rise. Warm water at 10 meters or 1000 meters still occupies more volume. Now it is possible pressure at 1000 meters squeezes warm water to a lessor volume and then my whole theory may be wrong. With a strong La Nina upwelling we may have water that is easier to warm. Based on the thought that 0.0 C sea water at the equator will warm easier than 30.0 C seawater. It will emit less warmth to the surface. With constant sunlight in it should hoard more warmth while cooling the atmosphere when compared to warmer water.
La Ninas seem to warm the ocean causing volume expansion. A large IPWP would seem to cause more sea level rise. What about healthy Pacific Gyre rotations? In the NH warm water goes North losing warmth and volume. Cool water goes South gaining warmth and volume. Like simultaneous El Nino and La Nina. Reduced Gyre rotations. Northern water stays the same however, assume sea ice forms because of reduced warm Southern water up there. Ice insulates and retains warmth, increasing volume. Equatorial water being warm emits more warmth to the atmosphere. Its storage of warmth is limited by how warm that seawater is.
While it might be obvious to others, I guess sea ice lose reduces sea level rise by cooling the oceans.