Sync rosters at match start, harden dedup and TIME handling, add scoreboard and damage summary

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <[email protected]>

lib/ui.py

@@ -431,6 +431,26 @@ def _draw_server_menu(screen, servers, names, selected):
     screen.refresh()
 
 
+def format_damage_summary(server_info):
+    """One-line damage summary (top 3 by damage dealt) from LIVESTATS counters;
+    None when no damage data exists yet. Dealt/taken are stored as strings."""
+    entries = []
+    for player_name, player_data in server_info.players.items():
+        try:
+            dealt = int(player_data.get('dealt', 0))
+            taken = int(player_data.get('taken', 0))
+        except (TypeError, ValueError):
+            continue
+        if dealt <= 0 and taken <= 0:
+            continue
+        entries.append((strip_color_codes(player_name), dealt, taken))
+    if not entries:
+        return None
+    entries.sort(key=lambda x: x[1], reverse=True)
+    summary = '   '.join(f"{name} {dealt}/{taken}" for name, dealt, taken in entries[:3])
+    return f"^8^3DMG^7 {summary}\n"
+
+
 class UIManager:
     """Manages curses windows and display"""
 
@@ -872,6 +892,11 @@ class UIManager:
                 line = f"^8{col1}^0{' ' * col1_pad}^8{col2}^0\n"
                 print_colored(self.info_window, line, 0)
 
+        # Damage summary from LIVESTATS counters (top 3 by damage dealt)
+        damage_line = format_damage_summary(server_info)
+        if damage_line:
+            print_colored(self.info_window, damage_line, 0)
+
         # Blank lines to fill
         try:
             self.info_window.addstr("\n")