Extract shared chat/settings/dialog CSS into chat.css

- Create chat.css with all shared chat panel, settings popover,
  dialog, toast, and animation styles (~730 lines)
- Remove ~840 lines of duplicate CSS from each demo
- Fix chat-quick-actions to flex-wrap across all demos
- Fix buggy var(--size-small/large) references in countries chat CSS
- Remove dead CSS (chat-utility-bar, api-key-bar, model-select, etc.)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: jonasneves