feat: Add SuperIntern AI chat widget

[aiden-cao]

PR Description

Summary

This PR integrates the SuperIntern “Ask AI” chat experience into the docs site and replaces the previous AI widget implementation.

What changed

• Added a new SuperIntern integration script (docs/assets/js/superintern.js) to initialize the AI chat button and hook it to the existing floating UI trigger (.ai-bot-wrapper).
• Removed the prior Inkeep custom button implementation (docs/assets/js/inkeep-custom-button.js).
• Included SPA/navigation re-bind handling so the click binding continues to work across route changes.
• Preserved analytics tracking on the floating button click (via dataLayer event).

Testing / Verification

• Load the docs site and confirm the floating AI button opens the chat modal
• Navigate between pages (SPA behavior) and confirm the button still works
• Confirm analytics event is emitted on click (if dataLayer is present)

Notes for reviewers

• Please verify the integration does not expose any sensitive configuration in the built site and that all keys/config are sourced appropriately for production.