feat: Story 14 - Auto-focus chat input on startup

Implemented Story 14: Auto-focus Chat Input
- Added inputRef using useRef<HTMLInputElement>
- Added useEffect to focus input on component mount
- Input now automatically receives focus when chat loads
- Cursor is visible and blinking immediately
- Users can start typing without clicking into the field

Updated Specs
- Added Input Focus Management section to UI_UX.md
- Specified auto-focus behavior and requirements
- Provided implementation example

.living_spec/stories/archive/14_put_cursor_in_chat_box_on_startup.md

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+# Story: Auto-focus Chat Input on Startup
+
+## User Story
+**As a** User
+**I want** the cursor to automatically appear in the chat input box when the app starts
+**So that** I can immediately start typing without having to click into the input field first.
+
+## Acceptance Criteria
+*   [x] When the app loads and a project is selected, the chat input box should automatically receive focus
+*   [x] The cursor should be visible and blinking in the input field
+*   [x] User can immediately start typing without any additional clicks
+*   [x] Focus should be set after the component mounts
+*   [x] Should not interfere with other UI interactions
+
+## Out of Scope
+*   Auto-focus when switching between projects (only on initial load)
+*   Remembering cursor position across sessions
+*   Focus management for other input fields
+
+## Implementation Notes
+*   Use React `useEffect` hook to set focus on component mount
+*   Use a ref to reference the input element
+*   Call `inputRef.current?.focus()` after component renders
+*   Ensure it works consistently across different browsers
+
+## Related Functional Specs
+*   Functional Spec: UI/UX