There are only two campaign plots

[Aliquid]

Solving a mystery is a variant of exploring the unknown, itself a variant of build an Empire/make money; the presence (or lack thereof) of a Dark Lord only changes peripherals on the "explore/build" paradigm.

I can buy that solving a mystery is a variant of exploring the unknown. You might not be exploring an unknown location, but you are exploring an issue with an unknown answer.

But I don't agree that it has to be a variant on building an empire/making money. You can easily have a mystery to solve and not make a profit or build an empire in the process.

With "solve a mystery" and "explore the unknown" I feel that it still needs to answer the question why the player characters would care. What would they accomplish if they succeed and why would it be a problem if they don't?

Depends on the player. Personally I'm a curious person, so I'm happy to explore for the sake of exploring.

I think Exploration most often is a more specific case of Treasure Hunt, while Mystery is often the beginning part of Invasion (You rarely know the villain plans an invasion of soldiers/demons/undead right from the start; that's commonly the answer to the mystery.)

It typically is, but it doesn't have to be.