Update index to reflect current Prefect recs and fix an example

[discdiver]

Updates the docs index page to fix a broken example, reorder information, and improve the page.

Checklist

• References any related issue by including "Closes #" or "Closes ".
  • If no issue exists and your change is not a small fix, please create an issue first.
• Includes tests or only affects documentation.
• Passes pre-commit checks.
  • Run pre-commit install && pre-commit run --all locally for formatting and linting.
• Includes screenshots of documentation updates.
  • Run mkdocs serve view documentation locally.

[desertaxle]

Thanks @discdiver!