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Makes sense actually. Animals have had half a billion years: if photosynthesis could power them some of them would be using it.

The sloth actually supplements their diet with photosynthetic algae that live on their fur. But their metabolism is very very slow.

That would be equivalent to us carrying a lattice pot around and then eating the lattice. Not a real example of photosynthetic animals.

The solutions you describe are functionally identical, so I do not see why it wouldn't be a "real example".

There are undersea slugs who store devoured algeas chlorophyl in transparent pockets under the skin.