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/specs/functional/UI_UX.md

@@ -157,3 +157,35 @@ Integrate syntax highlighting into markdown code blocks rendered by the assistan
     ```
 *   Ensure syntax highlighted code blocks are left-aligned
 *   Test with various code samples to ensure proper rendering
+
+## Input Focus Management
+
+### Problem
+When the app loads with a project selected, users need to click into the chat input box before they can start typing. This adds unnecessary friction to the user experience.
+
+### Solution: Auto-focus on Component Mount
+The chat input field should automatically receive focus when the chat component mounts, allowing users to immediately start typing.
+
+### Requirements
+
+1. **Auto-focus:** Input field receives focus automatically when chat component loads
+2. **Visible Cursor:** Cursor should be visible and blinking in the input field
+3. **Immediate Typing:** User can start typing without clicking into the field
+4. **Non-intrusive:** Should not interfere with other UI interactions or accessibility
+5. **Timing:** Focus should be set after the component fully mounts
+
+### Implementation Notes
+*   Use React `useRef` to create a reference to the input element
+*   Use `useEffect` with empty dependency array to run once on mount
+*   Call `inputRef.current?.focus()` in the effect
+*   Ensure the ref is properly attached to the input element
+*   Example implementation:
+    ```tsx
+    const inputRef = useRef<HTMLInputElement>(null);
+    
+    useEffect(() => {
+      inputRef.current?.focus();
+    }, []);
+    
+    return <input ref={inputRef} ... />
+    ```