[EuiFlyout] Update docs and patterns

[ryankeairns]

Summary

Why are we making this change?

Screenshots #

Impact to users

QA

Remove or strikethrough items that do not apply to your PR.

General checklist

• Browser QA
  • [ ] Checked in both light and dark modes
  • [ ] Checked in both MacOS and Windows high contrast modes
    • (emulate forced colors if you do not have access to a Windows machine.)
  • [ ] Checked in mobile
  • [ ] Checked in Chrome, Safari, Edge, and Firefox
  • [ ] Checked for accessibility including keyboard-only and screenreader modes
• Docs site QA
  • [ ] Added documentation
  • [ ] Props have proper autodocs (using @default if default values are missing) and playground toggles
  • [ ] Checked Code Sandbox works for any docs examples
• Code quality checklist
  • [ ] Added or updated jest and cypress tests
  • [ ] Updated visual regression tests
• Release checklist
  • [ ] A changelog entry exists and is marked appropriately
  • [ ] If applicable, added the breaking change issue label (and filled out the breaking change checklist)
  • [ ] If the changes unblock an issue in a different repo, smoke tested carefully (see Testing EUI features in Kibana ahead of time)
• Designer checklist
  • [ ] If applicable, file an issue to update EUI's Figma library with any corresponding UI changes. (This is an internal repo, if you are external to Elastic, ask a maintainer to submit this request)