Improve client matchmaking flow with ticket handling, auto-join, and mode distribution

### PlayerWebSocketHandler updates
- Track `ticket` and `match_id` per player instance
- Handle `matchmaker_ticket` messages and store ticket
- Handle `matchmaker_matched` and automatically join created match
- Enhance matchmaking debug output
- Update join_matchmaking() to include mode-based string_properties + query

### Matchmaking simulation improvements
- Evenly distribute players between "classic" and "blitz" modes
- Randomize assignment order to simulate real queue behavior
- Log player→mode mapping for visibility during tests

Example:
  player_0 -> classic
  player_3 -> blitz
  player_5 -> classic

Client test harness now accurately reflects multi-mode matchmaking behavior.

match_making_flow.py

@@ -1,8 +1,9 @@
 import asyncio
-from game_flow import PlayerWebSocketHandler
+import random
+from game_flow import PlayerWebSocketHandler, TEST_SCENARIOS
 
 
-async def simulate_matchmaking(num_players: int = 6, mode: str = "classic"):
+async def simulate_matchmaking(num_players: int = 6):
     print(f"\n🎮 Spawning {num_players} players...\n")
 
     # 1) Login + WebSocket connect
@@ -21,12 +22,20 @@ async def simulate_matchmaking(num_players: int = 6, mode: str = "classic"):
 
     await asyncio.sleep(0.3)
 
-    # 3) Queue all players in matchmaking
-    print(f"\n🎯 Queuing players for mode={mode}...\n")
+    # ✅ 3) Split evenly between classic & blitz
+    half = num_players // 2
+    assignments = ["classic"] * half + ["blitz"] * (num_players - half)
+
+    # Optional — shuffle for realism
+    random.shuffle(assignments)
+
+    print("\n🎯 Queuing players:")
+    for p, mode in zip(players, assignments):
+        print(f" - {p.label} -> {mode}")
 
     await asyncio.gather(*[
         p.join_matchmaking(mode)
-        for p in players
+        for p, mode in zip(players, assignments)
     ])
 
     print("\n✅ All players queued — waiting for matches...\n")