[EPIC] Improve examples to make them easier to navigate about datafusion HOT 4 OPEN

I played around with what we have and it turns out I think we can test examples in the user guide. I made a PR with docs of how to do it: #11178

I think with that framework we could add many of the simpler examples directly into the documentation where they would be eaiser to find. We can leave the more complex ones in datafusion-examples perhaps

Thoughts?

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As a newcomer I'll say that this seems right to me. Examples that are right in the documentation are much more discoverable.

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While working with @lewiszlw in #11173 (comment) I think I came up with a better idea -- that is to update the user guide so they code examples are run / tested

Then we can move many/all of the examples from rust to the user guide, which will make them easier to find and navigate. 🏃

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I plan do to this as a background task, but realistically can't devote enough focus time to it now

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