But intelligence is the capacity to solve problems. If you can solve problems quickly, you are by definition intelligent

To solve any problems? Because when I run a computer simulation from a random initial state, that's technically the computer solving a problem it's never seen before, and it is trillions of times faster than me. Does that mean the computer is trillions of times more intelligent than me?

the ability to apply knowledge to manipulate one's environment or to think abstractly as measured by objective criteria (such as tests)

If we built a true super-genius AI but never let it leave a small container, is it not intelligent because WE never let it manipulate its environment? And regarding the tests in the Merriam Webster definition, I suspect it's talking about "IQ tests", which in practice are known to be at least partially not objective. Just as an example, it's known that you can study for and improve your score on an IQ test. How does studying for a test increase your "ability to apply knowledge"? I can think of some potential pathways, but we're basically back to it not being clearly defined.

In essence, what I'm trying to say is that even though we can write down some definition for "intelligence", it's still not a concept that even humans have a fantastic understanding of, even for other humans. When we try to think of types of non-human intelligence, our current models for intelligence fall apart even more. Not that I think current LLMs are actually "intelligent" by however you would define the term.