Add sequence number logging and duplicate detection

- Log UnfilteredResultCountAfter for each ActionResultResponse to help
  diagnose sync mismatches (gaps in sequence = messages never arrived)
- Add LogFlow sequence counter (#1, #2, #3...) to diagnose duplicate
  logging issue: if same seq# appears twice, two threads are processing
  same message; if seq# increments but lines appear doubled, it's a
  StreamWriter/Logger issue

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

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

src/main/csharp/net/eagle0/clients/unity/eagle0/Assets/Eagle/PersistentClientConnection.cs

@@ -45,10 +45,16 @@ namespace eagle {
         private readonly Logger _remoteEagleClientLogger = Logger.GetLogger("ConnectionLogger");
         private readonly Logger _timingsLogger = Logger.GetLogger("ConnectionLogger");
 
+        // Counter to diagnose duplicate logging - if logs show same seq# twice, two threads
+        // are processing the same message. If seq# increments but lines appear doubled,
+        // it's a StreamWriter/Logger issue.
+        private int _logFlowSeq = 0;
+
         /// <summary>Timestamped log for connection flow tracing.</summary>
         private void LogFlow(string message) {
+            var seq = Interlocked.Increment(ref _logFlowSeq);
             var ts = DateTime.UtcNow.ToString("HH:mm:ss.fff");
-            _remoteEagleClientLogger.LogLine($"[FLOW {ts}] {message}");
+            _remoteEagleClientLogger.LogLine($"[FLOW {ts}] #{seq} {message}");
         }
 
         private volatile bool _isConnecting = false;
@@ -763,8 +769,8 @@ namespace eagle {
                                            ? arResp.AvailableCommands.CommandsByProvince?.Count ?? 0
                                            : 0;
                     var status = arResp.ServerGameStatus?.Status.ToString() ?? "null";
-                    LogFlow($"UPDATE ActionResult game={gameUpdate.GameId} actionResults={arCount} " +
-                            $"startingState={hasStartingState} hasCommands={hasCommands} " +
+                    LogFlow($"UPDATE ActionResult game={gameUpdate.GameId} countAfter={arResp.UnfilteredResultCountAfter} " +
+                            $"actionResults={arCount} startingState={hasStartingState} hasCommands={hasCommands} " +
                             $"token={cmdToken} cmdProvinces={cmdCount} status={status}");
 
                     // Update result counts IMMEDIATELY on the gRPC thread, before enqueueing.