Adds Hamilton UI Example

[skrawcz]

Updates docs and references for it.

Changes

• examples
• docs to the example

How I tested this

• locally

Notes

Checklist

• PR has an informative and human-readable title (this will be pulled into the release notes)
• Changes are limited to a single goal (no scope creep)
• Code passed the pre-commit check & code is left cleaner/nicer than when first encountered.
• Any change in functionality is tested
• New functions are documented (with a description, list of inputs, and expected output)
• Placeholder code is flagged / future TODOs are captured in comments
• Project documentation has been updated if adding/changing functionality.