Separate AI Chatbot documentation from AI Assistant API

Problem/Motivation

Follow-up to:

🌱 Add ChatbackendInterface Active

To split out the AI Chatbot documentation from AI Assistant API docs.

See context in comments 2 and 5 of:

🐛 AI module documentation has warnings when running mkdocs serve Active

Steps to reproduce (required for bugs, but not feature requests)

Please provide information like AI modules enabled, which AI provider, browser, etc.

Proposed resolution

Once the parent issue is done, split the docs.

Remaining tasks

• Wait for parent
• Split docs, review and merge

Backporting this won't make sense unless the parent changes will be backported.

Optional: Other details as applicable (e.g., User interface changes, API changes, Data model changes)