feat(matchmaking): enable mode-based matchmaking and improve match initialization

- Added matchmaker configuration to local.yml with support for string property "mode"
- Enabled faster matchmaking via interval_ms and large ticket limit
- Broadcast initial match state when both players join
- Added detailed validation and logging for move processing
- Broadcast game-over and forfeit states immediately on player leave
- Improved MatchLoop robustness with change tracking and clearer diagnostics

local.yml

@@ -7,3 +7,10 @@ session:
 socket:
   max_message_size_bytes: 4096 # reserved buffer
   max_request_size_bytes: 131072
+matchmaker:
+  max_tickets: 10000
+  interval_ms: 100
+  query:
+    properties:
+      string:
+        mode: true