feat: Remember last selected DM conversation

Add localStorage persistence for Direct Messages page to remember and restore the last selected conversation when user returns to the page.

Changes:
- Save selected conversation to localStorage when user selects a conversation
- Restore last conversation on page load (if no URL parameter provided)
- Clear localStorage when user returns to empty state
- Updated README.md with persistence documentation
- Priority: URL parameter > localStorage > empty state

This improves UX by maintaining conversation context across page navigation, similar to how the main page remembers the selected channel.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

README.md

@@ -355,6 +355,11 @@ Access the Direct Messages feature:
 4. Press Enter or click Send
 5. Click "Back" button to return to the main chat view
 
+**Persistence:**
+- The app remembers your last selected conversation
+- When you return to the DM page, it automatically opens the last conversation you were viewing
+- This works similarly to how the main page remembers your selected channel
+
 **Note:** Only client contacts (CLI) are shown in the dropdown. Repeaters (REP), rooms (ROOM), and sensors (SENS) are automatically filtered out.
 
 **Message status indicators:**