Redesign the mobile chat input bar

[Quack6765]

Summary

• Redesign the mobile chat composer with progressive disclosure and a persistent control rail.
• Add auto-resizing and collapsible-toolbar behavior across chat views and shell layouts.
• Update design documentation and expand unit coverage for composer, scrolling, responsive toggles, and resize behavior.

Testing

• Added and updated unit tests covering the new chat composer and layout behavior.
• Not run (not requested).