Nuclear waste is like asbestos, it’s fine if you leave it alone. If the depth is sufficient that the water is fairly anoxic and the area is geologically stable it’s pretty safe.

However if the area is unstable or the ship can rust you can easily end up with a huge distributor of radioactive contamination. The effects depend on the substance and type of radiation.

Dumping of radioactive waste in the ocean has been banned since 1993. https://en.m.wikipedia.org/wiki/Ocean_disposal_of_radioactiv...

Radioactive material + lots of water = good. You eventually end up with homeopathic densities of radioactive material, plus water itself is good at attenuating radiation.

Radioactive material + lots of water + lots of life in that water = bad. Small life eats the material, larger life eats small life, and after a while you end up eating cesium for dinner.