Fix README links and update structure

[peanutfun]

Changes proposed in this PR:

• Fix links, have them point to new docs
• Update structure:
  • Make data API less prominent
  • Fewer "click here" links
  • Separate introduction from overview

NOTE: Merging into develop is okay. Broken links in main are fixed by redirects on ReadTheDocs.

PR Author Checklist

• Read the Contribution Guide
• Correct target branch selected (if unsure, select develop)
• Descriptive pull request title added
• Source branch up-to-date with target branch
• Documentation updated
• Tests updated
• Tests passing
• No new linter issues
• Changelog updated

PR Reviewer Checklist

• Read the Contribution Guide
• CLIMADA Reviewer Checklist passed
• Tests passing
• No new linter issues