Why did the smallest plankton survive best after the K-Pg impact darkened the oceans?

Answer: Their tiny bodies needed less energy when food became scarce.

Their tiny bodies needed less energy when food became scarce. ✓ — Low energy demand is the key. Tiny cells need less food and energy to keep a population going, so when photosynthesis faltered and food became scarce, they could persist where larger plankton struggled. The advantage is not hardness but needing little enough to outlast a long bottleneck.

Their rapid sinking carried them below the darkened surface waters. — Sinking faster might look like a way to escape the darkened surface, but plankton need light for photosynthesis. Moving below the lit layer usually makes food harder to find, not easier. Sinking organic matter can feed deep communities, but that does not keep a plankton population alive and reproducing near the surface.

Their thick mineral shells shielded them from crushing and predators. — Tough shells can help against predators or abrasion, so the idea is not foolish. But the darkened oceans mainly created a food and energy shortage, and a hard shell cannot replace the carbon lost when photosynthesis drops. Many shelled plankton groups also did poorly, so shell strength was not the deciding advantage.