What do Prismatic Stones do?

The important part is the limit. A core skill takes one Prismatic Stone upgrade, and that is it. So the choice is not really "when do I use this" but "on which Aniimo", and you want that decided before you spend it rather than after. A stone dropped on the first creature you like is gone from the one you end up actually building around.

What you get back is two things at once. The damage on the core skill goes up, and the skill picks up utility it did not have before. That second part is why the upgrade is worth saving for a unit you intend to keep in rotation: raw numbers help anywhere, but a core skill that now does something extra changes how the Aniimo slots into a team.

Capability Fruit works on the same core skill, and it behaves differently in one way that matters. Capability Fruit upgrades transfer automatically to another Aniimo through inheritance. That investment is not locked to the creature you fed it to, which makes fruit the less nervous of the two materials to spend.

Getting hold of them

The Companion Collection bundle is one known source, and it is thin on these: one Prismatic Stone and one Capability Fruit, alongside one Prismana Orb and two Sparkling Cubes. One stone from a bundle is one core skill upgraded. Supply is what caps how many upgraded core skills you can field, not the cost of any single upgrade.

Not settled: Only the Capability Fruit side of the upgrade is known to carry across inheritance. Whether a Prismatic Stone upgrade follows an Aniimo the same way is not settled.