Chat — Support widget

Create chat — support widget.

Spec: Floating support chat widget with agent avatar.

Build with:
- Tailwind 4 + shadcn/ui primitives
- Fully responsive (stacks on mobile)
- Dark mode via next-themes
- Accessible: labels, aria where needed, keyboard nav
- TypeScript props

Return a single self-contained React component. Include mock data inline so it renders standalone.