Implements Telegram-like behavior for new messages:
1. Smart Auto-scroll (WS messages):
✅ User at bottom + present time → auto-scroll to new message
✅ User NOT at bottom + present time → show unread badge
❌ Historical view (hasMoreAfter=true) → no action
2. Smart Scroll Button (#scrollBtn):
- Shows unread badge when new messages arrive
- Click behavior:
* Has unread + lastReadId → scroll to first unread
* No unread → scroll to bottom
- Auto-hides badge when user scrolls to bottom
3. Badge Styling:
- Red badge with count on top-right of button
- Pulse animation on appearance
- Button subtle pulse when has unread
Key Logic:
- Only auto-scroll when hasMoreAfter=false (present time)
- Historical bottom (hasMoreAfter=true) doesn't trigger auto-scroll
- Badge resets on: manual scroll to bottom, button click
- Respects user's scroll position unless at bottom