feat(ui): add prompt queuing system and improve session management

- Add prompt queue to handle multiple prompts when Claude is processing
- Improve session reconnection with better event listener management
- Fix race conditions in session initialization and cleanup
- Replace Loader2 with rotating symbol for consistent loading states
- Remove TokenCounter integration and loading-disabled input restrictions
- Enhance cancellation logic with proper state cleanup
- Update thinking mode phrase formatting in FloatingPromptInput
- Improve UI layout with better spacing and error positioning

This enables users to queue multiple prompts without waiting for the current
one to complete, providing a smoother interaction experience.

Author: mufeedvh