[Re-bin]

Summary

• replace the sidebar wordmark with the existing nanobot cat icon
• keep a desktop collapsed sidebar rail instead of hiding the sidebar completely
• make the expanded and collapsed sidebar share one DOM structure so icons stay anchored during collapse
• keep the header theme toggle pinned to the page top-right while the desktop sidebar toggle is hidden

Why

The previous collapse behavior felt jumpy because the collapsed rail behaved like a separate UI. This keeps the logo and primary action icons in stable positions while only labels, chat history, and width collapse.

Validation

• npm run build
• npm run test
• browser check for desktop collapse/expand icon coordinates and mobile layout